Stability-robustness analysis for linear systems with state-space models精品.pdfVIP

Stability-robustness Analysis for Linear Systems with State-space Models hy HORNG-GIOU CHEN 0Zd KUANG-WEI HAN Institute of Electronics, National Chiao-Tung University, Hsinchu, Taiwan, R.O.C. ABSTRACT: The stability-robustness analysis for linear systems with state-space models is considered, The jiindamental problem of linear control systems subject to unstructured perturbations is addressed, and the results are extended to the consideration oj’linear control systems subject to linear structured perturbations. A modtjied time-domain Lyapunov-based method of stability-robustness analysis is proposed where iterative interpolations ofquadratic Lyapunov,functions are considered. By use ojthe proposed method, less conservative allowable perturbation bounds are obtained, and the resulting Lyaapunov matrices possess structural injormations closely related to the perturbation-susceptible characteristics of’ the nominal system state matrix. The robustness behaviour of‘ a vertical takeof and landing (VTOL) aircraft control system, designed by use of the LQ R state:jeedback method, is illustrated. Notation We denote the identity matrix by I and the all zero matrix by 0. Given a vector XE [w”, we take (Ix11= (x’x)‘!‘. This induces the matrix norm 11MI1 = omax(M) where omax(.) denotes the operation of taking the largest singular value. The following matrix operations and matrix relations are denoted : square-root of positive-semidefinite matrix symmetric portion of square matrix matrix formed by replacing each entry of