ref_robust_control.bib

@book{ackermannRobustControlSystems1993,
  title = {Robust {{Control}}: {{Systems With Uncertain Physical Parameters}}},
  shorttitle = {Robust {{Control}}},
  author = {Ackermann, Jurgen and Bartlett, Andrew and Kaesbauer, Dieter},
  year = {1993},
  month = nov,
  series = {Communications and {{Control Engineering}}},
  publisher = {Springer-Verlag},
  address = {London ; New York},
  url = {https://link.springer.com/book/10.1007/978-1-4471-0207-6},
  isbn = {978-0-387-19843-9},
  langid = {english}
}

@book{amatoRobustControlLinear2006,
  title = {Robust {{Control}} of {{Linear Systems Subject}} to {{Uncertain Time-Varying Parameters}}},
  author = {Amato, Francesco},
  year = {2006},
  month = feb,
  series = {Lecture {{Notes}} in {{Control}} and {{Information Sciences}}},
  number = {325},
  publisher = {Springer},
  address = {Berlin},
  url = {https://link.springer.com/book/10.1007/3-540-33276-6},
  isbn = {978-3-540-23950-5},
  langid = {english}
}

@article{andoTotallyPositiveMatrices1987,
  title = {Totally Positive Matrices},
  author = {Ando, T.},
  year = {1987},
  month = may,
  journal = {Linear Algebra and its Applications},
  volume = {90},
  pages = {165--219},
  issn = {0024-3795},
  doi = {10.1016/0024-3795(87)90313-2},
  url = {http://www.sciencedirect.com/science/article/pii/0024379587903132},
  urldate = {2014-01-21},
  abstract = {Though total positivity appears in various branches of mathematics, it is rather unfamiliar even to linear algebraists, when compared with positivity. With some unified methods we present a concise survey on totally positive matrices and related topics.}
}

@book{barmishNewToolsRobustness1993,
  title = {New {{Tools}} for {{Robustness}} of {{Linear Systems}}},
  author = {Barmish, {\relax Ross}. B.},
  year = {1993},
  month = jun,
  edition = {1st Edition edition},
  publisher = {Macmillan Coll Div},
  address = {New York : Toronto : New York},
  isbn = {978-0-02-306055-7},
  langid = {english}
}

@article{bialasFewResultsConcerning2012,
  title = {A Few Results Concerning the {{Hurwitz}} Stability of Polytopes of Complex Polynomials},
  author = {Bia{\l}as, Stanis{\l}aw and G{\'o}ra, Micha{\l}},
  year = {2012},
  month = mar,
  journal = {Linear Algebra and its Applications},
  volume = {436},
  number = {5},
  pages = {1177--1188},
  issn = {0024-3795},
  doi = {10.1016/j.laa.2011.07.042},
  url = {http://www.sciencedirect.com/science/article/pii/S0024379511005878},
  urldate = {2014-01-21},
  abstract = {Let C f 1 , {\dots} , f m be a polytope generated by complex polynomials f 1 , {\dots} , f m whose degrees differ at most by one. The main goal of this note is to provide a tool for verifying whether a polynomial family C f 1 , {\dots} , f m is stable. The note extend a few important results of the robust stability theory (the Edge Theorem given by Bartlett et al. (1988) [5], its generalizations proposed by Sideris and Barmish (1989) [7] and Fu and Barmish (1989) [6] and the eigenvalue criterions of Bia{\l}as (1985, 2004) [4,11]) to more general cases concerning complex polynomial families without degree-invariant assumptions. Numerical examples are presented to complete and illustrate the results.}
}

@article{boseTestsHurwitzSchur1989,
  title = {Tests for {{Hurwitz}} and {{Schur}} Properties of Convex Combination of Complex Polynomials},
  author = {Bose, N.K.},
  year = {1989},
  journal = {IEEE Transactions on Circuits and Systems},
  volume = {36},
  number = {9},
  pages = {1245--1247},
  issn = {0098-4094},
  doi = {10.1109/31.34672},
  abstract = {A test of Hurwitz (Schur) stability of a convex combination of Hurwitz (Schur) polynomials that requires only the checking for absence of zeros in the interval, 0{$<\lambda<$}1, of a polynomial in {$\lambda$} having complex coefficients is studied. From this polynomial {$\Delta$}({$\lambda$}) a polynomial {$\Delta$}*({$\lambda$}) can be constructed by complex conjugating the coefficients of {$\Delta$}({$\lambda$}) in order to form a polynomial which has real coefficients. When the coefficients are restricted to real coefficients, a simplification is provided that is particularly attractive since the Hurwitz stability of a convex combination of strict Hurwitz nth-degree polynomials requires the testing for the absence of zeros in the real interval (0, 1) of a polynomial of degree (n-1). A similar statement applies to a specialization of the results pertaining to Schur stability when the polynomial coefficients are real. This study, therefore, provides a unified approach for testing the Hurwitz or Schur stability of a convex combination of polynomials and generalizes earlier results to the complex coefficient case}
}

@article{burkeStabilizationNonsmoothNonconvex2006,
  title = {Stabilization via {{Nonsmooth}}, {{Nonconvex Optimization}}},
  author = {Burke, J.V. and Henrion, D. and Lewis, A.S. and Overton, M.L.},
  year = {2006},
  month = nov,
  journal = {IEEE Transactions on Automatic Control},
  volume = {51},
  number = {11},
  pages = {1760--1769},
  issn = {0018-9286},
  doi = {10.1109/TAC.2006.884944},
  abstract = {Nonsmooth variational analysis and related computational methods are powerful tools that can be effectively applied to identify local minimizers of nonconvex optimization problems arising in fixed-order controller design. We support this claim by applying nonsmooth analysis and methods to a challenging "Belgian chocolate" stabilization problem posed in 1994: find a stable, minimum phase, rational controller that stabilizes a specified second-order plant. Although easily stated, this particular problem remained unsolved until 2002, when a solution was found using an eleventh-order controller. Our computational methods find a stabilizing third-order controller without difficulty, suggesting explicit formulas for the controller and for the closed loop system, which has only one pole with multiplicity 5. Furthermore, our analytical techniques prove that this controller is locally optimal in the sense that there is no nearby controller with the same order for which the closed loop system has all its poles further left in the complex plane. Although the focus of the paper is stabilization, once a stabilizing controller is obtained, the same computational techniques can be used to optimize various measures of the closed loop system, including its complex stability radius or Hinfin performance}
}

@phdthesis{devriesIdentificationModelUncertainty1994,
  title = {Identification of {{Model Uncertainty}} for {{Control Design}}},
  author = {{de Vries}, Douwe Klaas},
  year = {1994},
  school = {TU Delft}
}

@book{doyleFeedbackControlTheory2009,
  title = {Feedback {{Control Theory}}},
  author = {Doyle, John C. and Francis, Bruce A. and Tannenbaum, Allen R.},
  year = {2009},
  month = jan,
  edition = {Reprint of the 1990 edition by Macmillan Publishing},
  publisher = {Dover Publications},
  url = {https://www.control.utoronto.ca/people/profs/francis/dft.pdf},
  isbn = {0-486-46933-6}
}

@book{dullerudCourseRobustControl2000,
  title = {A {{Course}} in {{Robust Control Theory}}: {{A Convex Approach}}},
  shorttitle = {A {{Course}} in {{Robust Control Theory}}},
  author = {Dullerud, Geir E. and Paganini, Fernando},
  year = {2000},
  series = {Texts in {{Applied Mathematics}}},
  publisher = {Springer-Verlag},
  address = {New York},
  doi = {10.1007/978-1-4757-3290-0},
  url = {https://www.springer.com/gp/book/9780387989457},
  urldate = {2021-04-16},
  abstract = {Research in robust control theory has been one of the most active areas of mainstream systems theory since the late 70s. This research activity has been at the confluence of dynamical systems theory, functional analysis, matrix analysis, numerical methods, complexity theory, and engineering applications. The discipline has involved interactions between diverse research groups including pure mathematicians, applied mathematicians, computer scientists and engineers. This research effort has produced a rather extensive set of approaches using a wide variety of mathematical techniques, and applications of robust control theory are spreading to areas as diverse as control of fluids, power networks, and the investigation of feddback mechanisms in biology. During the 90's the theory has seen major advances and achieved a new maturity, centered around the notion of convexity. The goal of this book is to give a graduate-level course on robust control theory that emphasizes these new developments, but at the same time conveys the main principles and ubiquitous tools at the heart of the subject. Its pedagogical objectives are to introduce a coherent and unified framework for studying robust control theory, to provide students with the control-theoretic background required to read and contribute to the research literature, and to present the main ideas and demonstrations of the major results of robust control theory. The book will be of value to mathematical researchers and computer scientists wishing to learn about robust control theory, graduate students planning to do research in the area, and engineering practitioners requiring advanced control techniques.},
  isbn = {978-0-387-98945-7},
  langid = {english}
}

@article{dumitrescuRobustSchurStability2006,
  title = {Robust Schur Stability with Polynomial Parameters},
  author = {Dumitrescu, B. and Chang, Bor-Chin},
  year = {2006},
  month = jul,
  journal = {IEEE Transactions on Circuits and Systems II: Express Briefs},
  volume = {53},
  number = {7},
  pages = {535--537},
  issn = {1558-3791},
  doi = {10.1109/TCSII.2006.875329},
  abstract = {We propose a stability test for discrete-time systems whose coefficients depend polynomially on some bounded parameters. The test is a particular form of Positivstellensatz, appeals to sum-of-squares polynomials and can be implemented as a semidefinite programming problem. Although implementable only in relaxed form, due to the necessity of limiting the degrees of the polynomial variables involved, the experiments show a good accuracy with degrees smaller than for other tests}
}

@inproceedings{ermTimeGoHinfinity2004,
  title = {Time to Go {{H-infinity}}?},
  booktitle = {Proceedings of {{SPIE}}},
  author = {Erm, Toomas},
  year = {2004},
  pages = {68--78},
  address = {Glasgow, Scotland, United Kingdom},
  doi = {10.1117/12.555606},
  url = {http://link.aip.org/link/?PSI/5496/68/1&Agg=doi},
  urldate = {2011-06-13}
}

@book{gershonHinfinityControlEstimation2005,
  title = {H-Infinity {{Control}} and {{Estimation}} of {{State-multiplicative Linear Systems}}},
  author = {Gershon, Eli and Shaked, Uri and Yaesh, Isaac},
  year = {2005},
  month = jun,
  edition = {2005 edition},
  publisher = {Springer},
  address = {London},
  abstract = {Multiplicative noise appears in systems where the process or measurement noise levels depend on the system state vector. Such systems are relevant, for example, in radar measurements where larger ranges involve higher noise level. This monograph embodies a comprehensive survey of the relevant literature with basic problems being formulated and solved by applying various techniques including game theory, linear matrix inequalities and Lyapunov parameter-dependent functions. Topics covered include: convex H2 and H-infinity norms analysis of systems with multiplicative noise; state feedback control and state estimation of systems with multiplicative noise; dynamic and static output feedback of stochastic bilinear systems; tracking controllers for stochastic bilinear systems utilizing preview information.  Various examples which demonstrate the applicability of the theory to practical control engineering problems are considered; two such examples are taken from the aerospace and guidance control areas.},
  isbn = {978-1-85233-997-5},
  langid = {english}
}

@book{guRobustControlDesign2013,
  title = {Robust {{Control Design}} with {{MATLAB}}{\textregistered}},
  author = {Gu, Da-Wei and Petkov, Petko H. and Konstantinov, Mihail M.},
  year = {2013},
  month = may,
  series = {Advanced {{Textbooks}} in {{Control}} and {{Signal Processing}}},
  edition = {2},
  publisher = {Springer},
  address = {New York},
  url = {https://doi.org/10.1007/978-1-4471-4682-7},
  abstract = {New edition offers improved guidance in robust control design for the graduate student and practising engineer Step-by-step explanation of MATLAB{\textregistered} Robust Control Toolbox 3 Practical examples show the reader how to take fullest advantage of an important and popular form of control in a variety of systems Insightful analysis of real design experience with only the theoretical essentials allows for a straightforward teaching and learning approach M-files, mdl-files and s-functions help to replicate example results and facilitate their adaptation for use in the reader's own study End-of-chapter exercises and electronic solutions manual aid the teacher in preparing courses},
  isbn = {978-1-4471-4681-0},
  langid = {english}
}

@article{henrionEllipsoidalApproximationStability2003,
  title = {Ellipsoidal Approximation of the Stability Domain of a Polynomial},
  author = {Henrion, D. and Peaucelle, D. and Arzelier, D. and Sebek, M.},
  year = {2003},
  month = dec,
  journal = {IEEE Transactions on Automatic Control},
  volume = {48},
  number = {12},
  pages = {2255--2259},
  issn = {0018-9286},
  doi = {10.1109/TAC.2003.820161},
  url = {http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=1254101},
  urldate = {2014-03-01}
}

@article{holtzHermiteBiehlerRouth2003,
  title = {Hermite--{{Biehler}}, {{Routh}}--{{Hurwitz}}, and Total Positivity},
  author = {Holtz, Olga},
  year = {2003},
  month = oct,
  journal = {Linear Algebra and its Applications},
  volume = {372},
  pages = {105--110},
  issn = {0024-3795},
  doi = {10.1016/S0024-3795(03)00501-9},
  url = {http://www.sciencedirect.com/science/article/pii/S0024379503005019},
  urldate = {2014-01-21},
  abstract = {Simple proofs of the Hermite--Biehler and Routh--Hurwitz theorems are presented. The total nonnegativity of the Hurwitz matrix of a stable real polynomial follows as an immediate corollary.}
}

@article{hwangUseRouthArray2001,
  title = {The Use of {{Routh}} Array for Testing the {{Hurwitz}} Property of a Segment of Polynomials},
  author = {Hwang, Chyi and Yang, Shih-Feng},
  year = {2001},
  month = feb,
  journal = {Automatica},
  volume = {37},
  number = {2},
  pages = {291--296},
  issn = {0005-1098},
  doi = {10.1016/S0005-1098(00)00142-4},
  url = {http://www.sciencedirect.com/science/article/pii/S0005109800001424},
  urldate = {2014-01-21},
  abstract = {In this paper we show that the test of Hurwitz property of a segment of polynomials (1-{$\lambda$})p0(s)+{$\lambda$}p1(s), where {$\lambda\in$}[0,1], p0(s) and p1(s) are nth-degree polynomials of real coefficients, can be achieved via the approach of constructing a fraction-free Routh array and using Sturm's theorem. We also establish the connection between the proposed approach and the finite-step methods based on the resultant theory and the boundary crossing theorem. In a certain sense, the proposed approach provides an efficient numerical implementation of the later two methods and, therefore, by which the robust Hurwitz stability of convex combinations of polynomials can be checked in a definitely finite number of arithmetic operations without having to invoke any root-finding procedure.}
}

@article{jonssonRobustnessPeriodicTrajectories2002,
  title = {Robustness of Periodic Trajectories},
  author = {Jonsson, U.T. and {Chung-Yao Kao} and Megretski, A.},
  year = {2002},
  journal = {Automatic Control, IEEE Transactions on},
  volume = {47},
  number = {11},
  pages = {1842--1856},
  issn = {0018-9286},
  doi = {10.1109/TAC.2002.804480},
  abstract = {A robustness problem for periodic trajectories is considered. A nonautonomous system with a periodic solution is given. The problem is to decide whether a stable periodic solution remains in a neighborhood of the nominal periodic solution when the dynamics of the system is perturbed. The case with a structured dynamic perturbation is considered. This makes the problem a nontrivial generalization of a classical problem in the theory of dynamical systems. A solution to the robustness problem will be obtained by using a variational system obtained by linearizing the system dynamics along a trajectory, which is uncertain but within the prespecified neighborhood of the nominal trajectory. This gives rise to robustness conditions that can be solved using integral quadratic constraints for linear time periodic systems.}
}

@article{lanzonDistanceMeasuresUncertain2009,
  title = {Distance {{Measures}} for {{Uncertain Linear Systems}}: {{A General Theory}}},
  shorttitle = {Distance {{Measures}} for {{Uncertain Linear Systems}}},
  author = {Lanzon, A. and Papageorgiou, G.},
  year = {2009},
  month = jul,
  journal = {IEEE Transactions on Automatic Control},
  volume = {54},
  number = {7},
  pages = {1532--1547},
  issn = {0018-9286},
  doi = {10.1109/TAC.2009.2022098},
  abstract = {In this paper, we propose a generic notion of distance between systems that can be used to measure discrepancy between open-loop systems in a feedback sense under several uncertainty structures. When the uncertainty structure is chosen to be four-block (or equivalently, normalized coprime factor) uncertainty, then this generic distance measure reduces to the well-known nu-gap metric. Associated with this generic distance notion, we also define a generic stability margin notion that allows us to give the distance measure a feedback interpretation by deriving generic robust stability and robust performance results. The proposed distance notion and the corresponding results exploit a powerful generalization of the small-gain theorem which handles perturbations in RfrL infin, rather than only in RfrH infin. When the uncertainty structure is fixed to one of the standard structures (e.g., additive, multiplicative, inverse multiplicative, coprime factor, four-block or any mixtures of the above), we give a step-by-step procedure (based on model validation ideas) that shows how the generic notion of distance and the correspondingly generic winding number conditions can be reduced to simple formulae. This work provides a unified framework that captures and embeds previous results in this area and also completes the picture by showing how other results of a similar nature can be obtained from the same framework. The techniques used involve only basic linear algebra, so they also provide a simplification of previous advanced proofs. Furthermore, the various distance measures so created can be used for non-conservative model embedding into the smallest uncertain family. An illustrative example is also given that demonstrates the superior qualities, above the nu-gap metric, of a particular distance measure obtained from this work in situations where the plant is lightly-damped. All systems considered in this paper are linear time-invariant.}
}

@book{lavretskyRobustAdaptiveControl2024,
  title = {Robust and {{Adaptive Control}}: {{With Aerospace Applications}}},
  shorttitle = {Robust and {{Adaptive Control}}},
  author = {Lavretsky, Eugene and Wise, Kevin},
  year = {2024},
  series = {Advanced {{Textbooks}} in {{Control}} and {{Signal Processing}} ({{C}}\&{{SP}})},
  edition = {2},
  publisher = {Springer},
  address = {Cham},
  url = {https://doi.org/10.1007/978-3-031-38314-4},
  abstract = {Robust and Adaptive Control shows the reader how to produce consistent and accurate controllers that operate in the presence of uncertainties and unforeseen events. Driven by aerospace applications the focus of the book is primarily on continuous-dynamical systems.~The text is a three-part treatment, beginning with robust and optimal linear control methods and moving on to a self-contained presentation of the design and analysis of model reference adaptive control (MRAC) for nonlinear uncertain dynamical systems. Recent extensions and modifications to MRAC design are included, as are guidelines for combining robust optimal and MRAC controllers. Features of the text include:{$\cdot~~~~~~~~$} case studies that demonstrate the benefits of robust and adaptive control for piloted, autonomous and experimental aerial platforms;{$\cdot~~~~~~~~$} detailed background material for each chapter to motivate theoretical developments;{$\cdot~~~~~~~~$} realistic examples and simulation data illustrating key features of the methods described; and{$\cdot~~~~~~~~$} problem solutions for instructors and MATLAB{\textregistered} code provided electronically.~The theoretical content and practical applications reported address real-life aerospace problems, being based on numerous transitions of control-theoretic results into operational systems and airborne vehicles that are drawn from the authors' extensive professional experience with The Boeing Company. The systems covered are challenging, often open-loop unstable, with uncertainties in their dynamics, and thus requiring both persistently reliable control and the ability to track commands either from a pilot or a guidance computer.Readers are assumed to have a basic understanding of root locus, Bode diagrams, and Nyquist plots, as well as linear algebra, ordinary differential equations, and the use of state-space methods in analysis and modeling of dynamical systems.Robust and Adaptive Control is intended to methodically teach senior undergraduate and graduate students how to construct stable and predictable control algorithms for realistic industrial applications. Practicing engineers and academic researchers will also find the book of great instructional value.},
  isbn = {978-3-031-38313-7},
  langid = {english}
}

@article{meinsmaElementaryProofRouthHurwitz1995,
  title = {Elementary Proof of the {{Routh-Hurwitz}} Test},
  author = {Meinsma, Gjerrit},
  year = {1995},
  month = jul,
  journal = {Systems \& Control Letters},
  volume = {25},
  number = {4},
  pages = {237--242},
  issn = {0167-6911},
  doi = {10.1016/0167-6911(94)00089-E},
  url = {http://www.sciencedirect.com/science/article/pii/016769119400089E},
  urldate = {2014-01-21},
  abstract = {This note presents an elementary proof of the familiar Routh-Hurwitz test. The proof is basically one continuity argument, it does not rely on Sturm chains, Cauchy index and the principle of the argument and it is fully self-contained. In the same style an extended Routh-Hurwitz test is derived, which finds the inertia of polynomials.}
}

@book{morariRobustProcessControl1989,
  title = {Robust Process Control},
  author = {Morari, Manfred and Zafiriou, Evanghelos},
  year = {1989},
  publisher = {Prentice Hall},
  address = {Englewood Cliffs, N.J.},
  isbn = {0-13-782153-0 978-0-13-782153-2 0-13-781956-0 978-0-13-781956-0},
  langid = {english}
}

@article{petersenRobustControlUncertain2014,
  title = {Robust Control of Uncertain Systems: {{Classical}} Results and Recent Developments},
  shorttitle = {Robust Control of Uncertain Systems},
  author = {Petersen, Ian R. and Tempo, Roberto},
  year = {2014},
  month = may,
  journal = {Automatica},
  volume = {50},
  number = {5},
  pages = {1315--1335},
  issn = {0005-1098},
  doi = {10.1016/j.automatica.2014.02.042},
  url = {http://www.sciencedirect.com/science/article/pii/S0005109814000806},
  urldate = {2015-11-03},
  abstract = {This paper presents a survey of the most significant results on robust control theory. In particular, we study the modeling of uncertain systems, robust stability analysis for systems with unstructured uncertainty, robustness analysis for systems with structured uncertainty, and robust control system design including H {$\infty$} control methods. The paper also presents some more recent results on deterministic and probabilistic methods for systems with uncertainty.}
}

@book{poznyakAttractiveEllipsoidsRobust2014,
  title = {Attractive {{Ellipsoids}} in {{Robust Control}}},
  author = {Poznyak, Alexander and Polyakov, Andrey and Azhmyakov, Vadim},
  year = {9 {\v r}{\'i}jna 2014},
  series = {Systems \& {{Control}}: {{Foundations}} \& {{Applications}}},
  publisher = {Birkh{\"a}user},
  address = {Cham},
  url = {https://doi.org/10.1007/978-3-319-09210-2},
  abstract = {This monograph introduces a newly developed robust-control design technique for a wide class of continuous-time dynamical systems called the ``attractive ellipsoid method.'' Along with a coherent introduction to the proposed control design and related topics, the monograph studies nonlinear affine control systems in the presence of uncertainty and presents a constructive and easily implementable control strategy that guarantees certain stability properties. The authors discuss linear-style feedback control synthesis in the context of the above-mentioned systems. The development and physical implementation of high-performance robust-feedback controllers that work in the absence of complete information is addressed, with numerous examples to illustrate how to apply the attractive ellipsoid method to mechanical and electromechanical systems. While theorems are proved systematically, the emphasis is on understanding and applying the theory to real-world situations. Attractive Ellipsoids in Robust Control will appeal to undergraduate and graduate students with a background in modern systems theory as well as researchers in the fields of control engineering and applied mathematics.},
  isbn = {978-3-319-09209-6}
}

@book{sanchez-penaRobustSystemsTheory1998,
  title = {Robust {{Systems Theory}} and {{Applications}}},
  author = {{S{\'a}nchez-Pe{\~n}a}, Ricardo S. and Sznaier, Mario},
  year = {1998},
  month = aug,
  edition = {1},
  publisher = {Wiley-Interscience},
  isbn = {0-471-17627-3}
}

@article{shammaRobustStabilityTimevarying1994,
  title = {Robust Stability with Time-Varying Structured Uncertainty},
  author = {Shamma, J.S.},
  year = {1994},
  journal = {Automatic Control, IEEE Transactions on},
  volume = {39},
  number = {4},
  pages = {714--724},
  issn = {0018-9286},
  doi = {10.1109/9.286248},
  abstract = {Considers the problem of assessing robust stability in the presence of block-diagonally structured time-varying dynamic uncertainty. It is shown that robust stability holds only if there exist constant scalings which lead to a small gain condition. The notion of stability here is finite-gain stability over finite-energy signals. In sharp contrast to the case of time-invariant dynamic uncertainty, this result is not limited by the number uncertainty blocks. These results parallel previous results regarding finite-gain stability over persistent bounded signals}
}

@article{shammaTimevaryingTimeinvariantCompensation1991,
  title = {Time-Varying versus Time-Invariant Compensation for Rejection of Persistent Bounded Disturbances and Robust Stabilization},
  author = {Shamma, J.S. and Dahleh, M.A.},
  year = {1991},
  journal = {Automatic Control, IEEE Transactions on},
  volume = {36},
  number = {7},
  pages = {838--847},
  issn = {0018-9286},
  doi = {10.1109/9.85063},
  abstract = {It is shown that time-varying compensation does not improve the optimal rejection of persistent bounded disturbances. This result is obtained by exploiting a key observation that any time-varying compensator which yields a given degree of disturbance rejection must do so uniformly over time, thereby removing any advantage of time-variation. This key observation is exploited to show that time-varying compensation does not improve the optimal rejection of disturbances, regardless of the norm used to measure the disturbances. Thus, absolutely summable, finite-energy, or persistent bounded disturbances may be treated in the same manner. It is shown that time-varying compensation does not help in the bounded-input bounded-output robust stabilization of time-invariant plants with unstructured uncertainty. In doing so, it is also shown that the small-gain theorem is both necessary and sufficient for the bounded-input bounded-output stability of certain linear time-varying plants subject to unstructured linear time-varying perturbations}
}

@book{schweppeUncertainDynamicSystems1973,
  title = {Uncertain Dynamic Systems},
  author = {Schweppe, Fred C.},
  year = {1973},
  month = jan,
  publisher = {Prentice-Hall},
  address = {Englewood Cliffs, N.J},
  isbn = {978-0-13-935593-6},
  langid = {english}
}

@article{titsCommentUseRouth2002,
  title = {Comment on ``{{The}} Use of {{Routh}} Array for Testing the {{Hurwitz}} Property of a Segment of Polynomials''},
  author = {Tits, Andre'e L.},
  year = {2002},
  month = mar,
  journal = {Automatica},
  volume = {38},
  number = {3},
  pages = {559--560},
  issn = {0005-1098},
  doi = {10.1016/S0005-1098(01)00220-5},
  url = {http://www.sciencedirect.com/science/article/pii/S0005109801002205},
  urldate = {2014-01-21},
  abstract = {It is pointed out that the main result in the paper ``The use of Routh array for testing the Hurwitz property of a segment of polynomials'' by Hwang and Yang (2001) is a known result.}
}

@article{tsaiJLosslessCoprimeFactorizations1991,
  title = {On {{J-Lossless}} Coprime Factorizations and {{H-infinity}} Control},
  author = {Tsai, Mi-Ching and Postlethwaite, Ian},
  year = {1991},
  journal = {International Journal of Robust and Nonlinear Control},
  volume = {1},
  number = {1},
  pages = {47--68},
  issn = {1099-1239},
  doi = {10.1002/rnc.4590010107},
  url = {http://onlinelibrary.wiley.com/doi/10.1002/rnc.4590010107/abstract},
  urldate = {2012-09-18},
  abstract = {This paper presents a relatively simple approach, based on chain scattering descriptions, to the synthesis of internally stabilizing controllers which result in a cost function with H{$\infty$} norm strictly less than a prespecified bound. State-space formulae for a generator of all suboptimal controllers are found by solving two coupled J-lossless coprime factorizations of a chain scattering matrix description. A mixed-sensitivity design problem is used to illustrate the solution procedure, and to demonstrate how in certain cases only one algebraic Riccati equation need be solved to get a solution.},
  copyright = {Copyright {\copyright} 1991 John Wiley \& Sons, Ltd.},
  langid = {english}
}

@book{vinnicombeUncertaintyFeedbackLoopShaping2000,
  title = {Uncertainty and {{Feedback}}, {{H Loop-Shaping}} and the {{V-Gap Metric}}},
  author = {Vinnicombe, Glenn},
  year = {2000},
  month = nov,
  publisher = {World Scientific Publishing Company},
  address = {London},
  url = {https://doi.org/10.1142/p140},
  abstract = {The principal reason for using feedback is to reduce the effect of uncertainties in the description of a system which is to be controlled. H-infinity loop-shaping is emerging as a powerful but straightforward method of designing robust feedback controllers for complex systems. However, in order to use this, or other modern design techniques, it is first necessary to generate an accurate model of the system (thus appearing to remove the reason for needing feedback in the first place). The v-gap metric is an attempt to resolve this paradox - by indicating in what sense a model should be accurate if it is to be useful for feedback design. This book develops in detail the H-infinity loop-shaping design method, the v-gap metric and the relationship between the two, showing how they can be used together for successful feedback design.},
  isbn = {978-1-86094-163-4},
  langid = {english}
}

@book{yedavalliRobustControlUncertain2014,
  title = {Robust {{Control}} of {{Uncertain Dynamic Systems}}: {{A Linear State Space Approach}}},
  shorttitle = {Robust {{Control}} of {{Uncertain Dynamic Systems}}},
  author = {Yedavalli, Rama K.},
  year = {2014},
  publisher = {Springer},
  address = {New York},
  url = {https://doi.org/10.1007/978-1-4614-9132-3},
  isbn = {978-1-4614-9131-6},
  langid = {english}
}

@article{zamesInputoutputFeedbackStability1996,
  title = {Input-Output Feedback Stability and Robustness, 1959-85},
  author = {Zames, G.},
  year = {1996},
  journal = {Control Systems Magazine, IEEE},
  volume = {16},
  number = {3},
  pages = {61--66},
  issn = {0272-1708},
  doi = {10.1109/37.506399},
  abstract = {The literature on input-output feedback is too large to do justice into a single article. Here we concentrate on the formative years ending in 1985 and leave the subsequent story to be told elsewhere. It is not a comprehensive survey of the literature or even of the most important papers. Rather, it is an attempt to describe events that marked the turning points. The period under scrutiny can be divided into roughly two parts; interest in nonlinear stability dominated the first part and robustness the second}
}

@book{zhouRobustOptimalControl1995,
  title = {Robust and {{Optimal Control}}},
  author = {Zhou, Kemin and Doyle, John C. and Glover, Keith},
  year = {1995},
  month = aug,
  edition = {1},
  publisher = {Prentice Hall},
  isbn = {0-13-456567-3}
}