Robust stability of multivariable systems with both real parametric and norm bounded uncertainties

The robust stability of a multivariable system with both structured real parametric and unstructured norm bounded uncertainties is considered. It is shown that if the real parametric uncertainty enters only linearly and independently into the numerator matrix and the denominator characteristic polynomial, then the robust stability (or stability margin) can be tested (or calculated) exactly. It is also shown that this in fact gives a way to compute a class of real structured singular values. >

[1]  G. Stein,et al.  Performance and robustness analysis for structured uncertainty , 1982, 1982 21st IEEE Conference on Decision and Control.

[2]  S. Bhattacharyya,et al.  Robust stability under structured and unstructured perturbations , 1990 .

[3]  J. Doyle.  Analysis of Feedback Systems with Structured Uncertainty , 1982 .

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

[5]  André L. Tits,et al.  On the robust stability of polynomials with no cross-coupling between the perturbations in the coefficients of even odd powers , 1989 .

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

[7]  J. Doyle,et al.  Structured singular value with repeated scalar blocks , 1988, 1988 American Control Conference.

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

[9]  E. Polak.  Introduction to linear and nonlinear programming , 1973 .

[10]  A. Tits,et al.  Characterization and efficient computation of the structured singular value , 1986 .

[11]  V. Kharitonov.  Asympotic stability of an equilibrium position of a family of systems of linear differntial equations , 1978 .

[12]  Stephen P. Boyd,et al.  A bisection method for computing the H∞ norm of a transfer matrix and related problems , 1989, Math. Control. Signals Syst..

[13]  M. Fan,et al.  A power method for the structured singular value , 1988, Proceedings of the 27th IEEE Conference on Decision and Control.