Robust Stability and Performance Analysis for the System with Linear Dependent Perturbations

Abstract In this paper, the sufficient conditions of the robust stability and robust performance for both continuous-time and discrete-time systems with structured perturbations are obtained using the matrix measure based approach. Using the derived results along with the Lyapunov based approach, several results for determining the robust criterion for the control system with time-varying perturbations are also obtained. Numerical examples have been given to illustrate the effectiveness of the proposed results. It shows that the proposed approach is less conservative than those proposed in the previous literature.

[1]  F. V. Vleck,et al.  Stability and Asymptotic Behavior of Differential Equations , 1965 .

[2]  J. Chou Pole-assignment robustness in a specified disk , 1991 .

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

[4]  J. Farison,et al.  Robust stability bounds on time-varying perturbations for state-space models of linear discrete-time systems , 1989 .

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

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

[7]  G. Dahlquist Stability and error bounds in the numerical integration of ordinary differential equations , 1961 .

[8]  A. Rachid Robustness of pole assignment in a specified region for perturbed systems , 1990 .

[9]  C. Desoer,et al.  Feedback Systems: Input-Output Properties , 1975 .

[10]  Ahmed Rachid,et al.  Robustness of discrete systems under structured uncertainties , 1989 .

[11]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[12]  Te-Son Kuo,et al.  New approach to time-domain analysis for stability robustness of dynamic systems , 1987 .

[13]  Shuenn-Shyang Wang,et al.  On the analysis of eigenvalue assignment robustness , 1992 .

[14]  Rama K. Yedavalli,et al.  Stability Robustness Measures under Dependent Uncertainty , 1988, 1988 American Control Conference.

[15]  Rama K. Yedavalli,et al.  Improved measures of stability robustness for linear state space models , 1985 .