STABILITY-ROBUSTNESS ANALYSIS FOR LINEAR-SYSTEMS WITH STATE-SPACE MODELS

Abstract

The stability-robustness analysis for linear systems with state-space models is considered. The fundamental problem of linear control systems subject to unstructured perturbations is addressed, and the results are extended to the consideration of linear control systems subject to linear structured perturbations. A modified time-domain Lyapunov-based method of stability-robustness analysis is proposed where iterative interpolations of quadratic Lyapunov functions are considered. By use of the proposed method, less conservative allowable perturbation bounds are obtained, and the resulting Lyapunov matrices possess structural informations closely related to the perturbation-susceptible characteristics of the nominal system state matrix. The robustness behaviour of a vertical takeoff and landing (VTOL) aircraft control system, designed by use of the LQR state-feedback method, is illustrated.