An overview of recent results on the parametric approach to robust stability

A discussion is presented of results relating to the parametric approach to robust stability. The general problem of robust stability is defined, and a review of Kharitonov-type and edge theorems, zero exclusion results, interval matrix stability, maximal perturbation bounds, multilinear and nonlinear perturbations, time delay systems, and numerical/graphical approaches is presented. Some open research directions are indicated, and the future of the approach is discussed.<<ETX>>

[1]  I. Horowitz Synthesis of feedback systems , 1963 .

[2]  Dragoslav D. Šiljak,et al.  Nonlinear systems;: The parameter analysis and design , 1968 .

[3]  Michael G. Safonov,et al.  Stability and Robustness of Multivariable Feedback Systems , 1980 .

[4]  G. Stein,et al.  Multivariable feedback design: Concepts for a classical/modern synthesis , 1981 .

[5]  B. Barmish Invariance of the strict Hurwitz property for polynomials with perturbed coefficients , 1983, The 22nd IEEE Conference on Decision and Control.

[6]  S. Bialas,et al.  Necessary and Sufficient Conditions for the Stability of Interval Matrices , 1983 .

[7]  A. Olbrot A sufficiently large time delay in feedback loop must destroy exponential stability of any decay rate , 1984 .

[8]  James A. Heinen,et al.  Sufficient conditions for stability of interval matrices , 1984 .

[9]  B. R. Barmish,et al.  Counter-example to a recent result on the stability of interval matrices by S. Bialas , 1984 .

[10]  J. Ackermann Sampled-Data Control Systems: Analysis and Synthesis, Robust System Design , 1985 .

[11]  Xu Daoyi Simple criteria for stability of interval matrices , 1985 .

[12]  C. B. Soh,et al.  On the stability properties of polynomials with perturbed coefficients , 1985 .

[13]  Jürgen Ackermann,et al.  Sampled-Data Control Systems , 1985 .

[14]  Jürgen Garloff,et al.  Convex combinations of stable polynomials , 1985 .

[15]  E. Davison,et al.  New perturbation bounds for the robust stability of linear state space models , 1986, 1986 25th IEEE Conference on Decision and Control.

[16]  R. Yedavalli,et al.  Reduced conservatism in stability robustness bounds by state transformation , 1986 .

[17]  J. Chiasson A Method for Computing the Interval of Delay Values for which a Differential-Delay System is Stable , 1988, 1986 American Control Conference.

[18]  E. Zeheb,et al.  On robust Hurwitz and Schur polynomials , 1986, 1986 25th IEEE Conference on Decision and Control.

[19]  D. Hinrichsen,et al.  Stability radii of linear systems , 1986 .

[20]  Christopher V. Hollot,et al.  Some discrete-time counterparts to Kharitonov's stability criterion for uncertain systems , 1986 .

[21]  S. Bhattacharyya,et al.  Robust stability with structured real parameter perturbations , 1987 .

[22]  Liao Xiao Xin,et al.  Stability of interval matrices , 1987 .

[23]  Christopher V. Hollot,et al.  Stability of families of polynomials: geometric considerations in coefficient space , 1987 .

[24]  M. Argoun Frequency domain conditions for the stability of perturbed polynomials , 1987 .

[25]  Sheng-De Wang,et al.  Root-locus approach to the stability analysis of interval matrices , 1987 .

[26]  Douglas Looze,et al.  Unmodeled dynamics: Performance and stability via parameter space methods , 1987, 26th IEEE Conference on Decision and Control.

[27]  Wei-Bin Gao,et al.  STABILITY OF INTERVAL PARAMETER MATRICES , 1987 .

[28]  Nirmal Kumar Bose,et al.  A simple general proof of Kharitonov's generalized stability criterion , 1987 .

[29]  Ian Peterson A class of stability regions for which a Kharitonov like theorem holds , 1987, 26th IEEE Conference on Decision and Control.

[30]  G. A. Hewer,et al.  Smallest destabilizing perturbations for linear systems , 1987 .

[31]  A. Levis,et al.  Challenges to control: A collective view--Report of the workshop held at the University of Santa Clara on September 18-19, 1986 , 1987 .

[32]  P. Khargonekar,et al.  Stability robustness bounds for linear state-space models with structured uncertainty , 1987 .

[33]  Ian R. Petersen,et al.  A new extension to Kharitonov's theorem , 1987 .

[34]  Te-Son Kuo,et al.  Stability robustness analysis of digital control systems in state-space models , 1987 .

[35]  Shankar P. Bhattacharyya,et al.  Robust Stabilization Against Structured Perturbations , 1987 .

[36]  J. Cieslik,et al.  On possibilities of the extension of Kharitonov's stability test for interval polynomials to the discrete-time case , 1987 .

[37]  C. Jiang Sufficient condition for the asymptotic stability of interval matrices , 1987 .

[38]  Huang Lin,et al.  Root locations of an entire polytope of polynomials: It suffices to check the edges , 1987, 1987 American Control Conference.

[39]  N. Bose,et al.  Network realizability theory approach to stability of complex polynomials , 1987 .

[40]  K. Wei,et al.  Invariance of a strict Hurwitz property for uncertain polynomials with dependent coefficients , 1987 .

[41]  Liao Xiao Xin,et al.  Necessary and sufficient conditions for stability of a class of interval matrices , 1987 .

[42]  K. Yeung,et al.  A simple proof of Kharitonov's theorem , 1987 .

[43]  Comment on ‘Stability of interval matrices’ , 1987 .

[44]  B. O. Anderson,et al.  Robust Schur polynomial stability and Kharitonov's theorem , 1987, 26th IEEE Conference on Decision and Control.

[45]  Mohammad B. Argoun,et al.  Stability of a Hurwitz polynomial under coefficient perturbations: necessary and sufficient conditions , 1987 .

[46]  R. Liu,et al.  A necessary and sufficient condition for stability of a perturbed system , 1987 .

[47]  B. Anderson,et al.  On robust Hurwitz polynomials , 1987 .

[48]  Bor-Sen Chen,et al.  Robust stability of uncertain time-delay systems , 1987 .

[49]  P. Dorato,et al.  A historical review of robust control , 1987, IEEE Control Systems Magazine.

[50]  Te-Son Kuo,et al.  Dynamic interval systems analysis and design , 1988 .

[51]  Edward J. Davison,et al.  A new method for the stability robustness determination of state space models with real perturbations , 1988, Proceedings of the 27th IEEE Conference on Decision and Control.

[52]  M. Mansour Sufficient conditions for the asymptotic stability of interval matrices , 1988 .

[53]  The pole placement theorem and small perturbations in parameters: the existence of an unassignable left half plane , 1988, Proceedings of the 27th IEEE Conference on Decision and Control.

[54]  Pramod P. Khargonekar,et al.  Robust stability of feedback control systems with uncertain parameters and unmodeled dynamics , 1988, 1988 American Control Conference.

[55]  Comments on ‘Sufficient and necessary condition for the asymptotic stability of discrete linear interval systems’ , 1988 .

[56]  Counter-examples to ‘Sufficient and necessary condition for the asymptotic stability of discrete linear interval systems’ , 1988 .

[57]  The minimal dimension of stable faces required to guarantee stability of a matrix polytope: D-stability , 1988, Proceedings of the 27th IEEE Conference on Decision and Control.

[58]  Jürgen Ackermann,et al.  Robustness analysis: a case study , 1988, Proceedings of the 27th IEEE Conference on Decision and Control.

[59]  M. Safonov,et al.  Exact calculation of the multiloop stability margin , 1988 .

[60]  Robin J. Evans,et al.  Stability analysis of interval matrices―continuous and discrete systems , 1988 .

[61]  E. Davison,et al.  Computation of the stability robustness of large state space models with real perturbations , 1988, Proceedings of the 27th IEEE Conference on Decision and Control.

[62]  Antonio Vicino,et al.  Some results on robust stability of discrete-time systems , 1988 .

[63]  B. Barmish A Generalization of Kharitonov's Four Polynomial Concept for Robust Stability Problems with Linearly Dependent Coefficient Perturbations , 1988, 1988 American Control Conference.

[64]  A. C. Bartlett,et al.  A necessary and sufficient condition for Schur invariance and generalized stability of polytopes of polynomials , 1988 .

[65]  A. W. Olbrot,et al.  A qualitative bound in robustness of stabilization by state feedback , 1988 .

[66]  C. B. Soh A simple method to check the stability of linear uncertain systems , 1988, Proceedings of the 27th IEEE Conference on Decision and Control.

[67]  R. Tempo,et al.  The robust root locus , 1988, Proceedings of the 27th IEEE Conference on Decision and Control.

[68]  Another sufficient condition for the stability of interval matrices , 1988 .

[69]  Yuval Bistritz,et al.  Stability criterion for continuous-time system polynomials with uncertain complex coefficients , 1988 .

[70]  A. Tits,et al.  Comment on ‘Sufficient condition for the asymptotic stability of interval matrices’ , 1988 .

[71]  N. K. Bose Robust stability of polynomials, univariate and multivariate: system-theoretic approach , 1988, Proceedings of the 27th IEEE Conference on Decision and Control.

[72]  Improved robust performance bounds in covariance majorant analysis , 1988, Proceedings of the 27th IEEE Conference on Decision and Control.

[73]  Dragoslav D. Šiljak,et al.  Robust stability of discrete systems , 1988 .

[74]  Shankar P. Bhattacharyya,et al.  Stability margins for Hurwitz polynomials , 1988, Proceedings of the 27th IEEE Conference on Decision and Control.

[75]  B. R. Barmish,et al.  Robust Schur stability of a polytope of polynomials , 1988 .

[76]  Eyad H. Abed,et al.  Robust stability of linear systems relative to guarded domains , 1988, Proceedings of the 27th IEEE Conference on Decision and Control.

[77]  R. Tempo The dual theorem of Kharitonov for a class of dependent uncertainties , 1988, Proceedings of the 27th IEEE Conference on Decision and Control.

[78]  A. Sideris,et al.  Robustness with real parametric and structured complex uncertainty , 1988, Proceedings of the 27th IEEE Conference on Decision and Control.

[79]  Z. Luo,et al.  Comments on ‘Sufficient condition for the asymptotic stability of interval matrices’ , 1988 .

[80]  Brian D. O. Anderson,et al.  Strong Kharitonov theorem for discrete systems , 1988, Proceedings of the 27th IEEE Conference on Decision and Control.

[81]  A. Vicino,et al.  Robustness analysis for uncertain dynamical systems with structured perturbations , 1988, Proceedings of the 27th IEEE Conference on Decision and Control.

[82]  Shaping conditions for the robust stability of polynomials with multilinear parameter uncertainty , 1988, Proceedings of the 27th IEEE Conference on Decision and Control.

[83]  On the robustness of root locations of polynomials under complex and real perturbations , 1988, Proceedings of the 27th IEEE Conference on Decision and Control.

[84]  Robust stability in linear state space models , 1988 .

[85]  Charles A. Desoer,et al.  Graphical stability robustness tests for linear time-invariant systems: generalizations of Kharitonov's stability theorem , 1988, Proceedings of the 27th IEEE Conference on Decision and Control.

[86]  Djordjija B. Petkovski Stability analysis of interval matrices: improved bounds , 1988 .

[87]  Antonio Vicino,et al.  An algorithm for nonconservative stability bounds computation for systems with nonlinearly correlated parametric uncertainties , 1988, Proceedings of the 27th IEEE Conference on Decision and Control.

[88]  R. Byers A Bisection Method for Measuring the Distance of a Stable Matrix to the Unstable Matrices , 1988 .

[89]  W. M. Grimm,et al.  Comments on "Reduced conservatism in stability robustness bounds by state transformation" [with reply] , 1988 .

[90]  Ricardo S. Sanchez Pena,et al.  Fast Computation of the Multivariable Stability Margin for Real Interrelated Uncertain Parameters , 1988 .

[91]  Diederich Hinrichsen,et al.  New robustness results for linear systems under real perturbations , 1988, Proceedings of the 27th IEEE Conference on Decision and Control.

[92]  B. Barmish New tools for robustness analysis , 1988, Proceedings of the 27th IEEE Conference on Decision and Control.

[93]  D. Siljak Parameter Space Methods for Robust Control Design: A Guided Tour , 1988, 1988 American Control Conference.

[94]  B. Barmish,et al.  Maximal unidirectional perturbation bounds for stability of polynomials and matrices , 1988 .

[95]  Chung-Li Jiang Sufficient and necessary condition for the asymptotic stability of discrete linear interval systems , 1988 .

[96]  B. R. Barmish,et al.  Stability of a polytope of matrices: counterexamples , 1988 .

[97]  The Largest Stability Hypercube for Families of Polynomials with Linear Uncertainty , 1989, 1989 American Control Conference.

[98]  A. Olbrot,et al.  Introduction to the parametric approach to robust stability , 1989, IEEE Control Systems Magazine.

[99]  Comments on ‘Robust stability in linear state space models’ , 1989 .

[100]  C. B. Soh One extending hypersphere method to handle dominant pole assignment , 1989 .

[101]  Athanasios Sideris A Polynomial time Algorithm for Checking the Robust Stability of a Polytope of Polynomials , 1989, 1989 American Control Conference.

[102]  Dennis S. Bernstein,et al.  Robust Stability for Sampled-Data Control Systems , 1989 .

[103]  B. Barmish,et al.  Polytopes of polynomials with zeros in a prescribed set , 1989 .

[104]  Yeng Chai Soh Strict Hurwitz property of polynomials under coefficient perturbation , 1989 .

[105]  Comments on ‘Sufficient and necessary condition for the asymptotic stability of discrete linear interval systems’ , 1989 .

[106]  C. V. Hollot Kharitonov-like results in the space of Markov parameters , 1989 .

[107]  Shankar P. Bhattacharyya,et al.  An alternative proof of Kharitonov's theorem , 1989 .

[108]  B. Ross Barmish,et al.  Robust stability of perturbed systems with time delays, , 1989, Autom..

[109]  Approximations of Robust Stability of Polynomials , 1989, 1989 American Control Conference.

[110]  Yau-Tarng Juang,et al.  Sufficient condition for asymptotic stability of discrete interval systems , 1989 .

[111]  A. Olbrot,et al.  Robust stability for time-delay systems: the edge theorem and graphical tests , 1989 .

[112]  A Class of Kharitonov Regions for Robust Stability of Linear Uncertain Systems , 1989, 1989 American Control Conference.

[113]  Comments on ‘Smallest destabilizing perturbations for linear systems’ , 1989 .

[114]  C. B. Soh,et al.  Strict aperiodic property of polynomials with perturbed coefficients , 1989 .

[115]  Comments on ‘Robust stability in linear state space models’ , 1989 .

[116]  C. DeMarco,et al.  The minimal dimension of stable faces required to guarantee stability of a matrix polytope , 1989 .

[117]  C. V. Hollot,et al.  The stability of a family of polynomials can be deduced from a finite number 0(k/sup 3/) of frequency checks , 1989 .

[118]  Counter-examples to Jiang's results , 1989 .

[119]  Comments on ‘Sufficient and necessary condition for the asymptotic stability of discrete linear interval systems’ , 1989 .

[120]  A Routh-Like Test for the Stability of Families of Polynomials with Linear Uncertainty , 1989 .

[121]  S. Bhattacharyya,et al.  A generalization of Kharitonov's theorem; Robust stability of interval plants , 1989 .

[122]  Yau-Tarng Juang,et al.  Stability analysis of dynamic interval systems , 1989 .

[123]  Alfredo C. Desages,et al.  Calculation of highly structured stability margins , 1989 .

[124]  Stability of an entire polytope of polynomials , 1989 .

[125]  Minyue Fu Polytopes of Polynomials with Zeros in a Prescribed Region: New Criteria and Algorithms , 1989 .

[126]  Andrzej W. Olbrot,et al.  Robust Design and Analysis of Third and Fourth Order Time Delay Systems with Application to Automotive Idle Speed Control , 1989, 1989 American Control Conference.

[127]  C. Desoer,et al.  An elementary proof of Kharitonov's stability theorem with extensions , 1989 .

[128]  D. Hyland,et al.  A Majorant Approach to Robust Stability and Time-Domain Performance Analysis for Discrete-Time Systems , 1989, 1989 American Control Conference.

[129]  Comment on ‘On sufficient conditions for the stability of interval matrices’ , 1989 .

[130]  Ezra Zeheb,et al.  Necessary and sufficient conditions for root clustering of a polytope of polynomials in a simply connected domain , 1989 .

[131]  Reduced conservatism of eigenvalue estimation , 1989 .

[132]  Antonio Vicino,et al.  Maximal polytopic stability domains in parameter space for uncertain systems , 1989 .

[133]  Counter-example to ‘Sufficient and necessary condition for the asymptotic stability of discrete linear interval systems’ , 1989 .

[134]  Roberto Tempo,et al.  Robust stability with multilinear perturbations: how good is the convex hull approximation? , 1990, 29th IEEE Conference on Decision and Control.

[135]  L. R. Pujara,et al.  On the stability of uncertain polynomials with dependent coefficients , 1990 .

[136]  Minyue Fu,et al.  The edge theorem and graphical tests for robust stability of neutral time-delay systems , 1989, Autom..

[137]  B. Anderson,et al.  Frequency domain conditions for the robust stability of linear and nonlinear dynamical systems , 1991 .