tailieunhanh - Báo cáo " Stability Radii for Difference Equations with Time-varying Coefficients "

This paper deals with a formula of stability radii for an linear difference equation (LDEs for short) with the coefficients varying in time under structured parameter perturbations. It is shown that the lp− real and complex stability radii of these systems coincide and they are given by a formula of input-output operator. The result is considered as an discrete version of a previous result for time-varying ordinary differential equations [1]. Keywords: Robust stability, Linear difference equation, Input-output operator, Stability radius . | VNU Journal of Science Mathematics - Physics 26 2010 175-184 Stability Radii for Difference Equations with Time-varying Coefficients Le Hong Lan Department of Basic Sciences University of Transport and Communication Hanoi Vietnam Received 10 August 2010 Abstract. This paper deals with a formula of stability radii for an linear difference equation LDEs for short with the coefficients varying in time under structured parameter perturbations. It is shown that the lp- real and complex stability radii of these systems coincide and they are given by a formula of input-output operator. The result is considered as an discrete version of a previous result for time-varying ordinary differential equations 1 . Keywords Robust stability Linear difference equation Input-output operator Stability radius 1. Introduction Many control systems are subject to perturbations in terms of uncertain parameters. An important quantitative measure of stability robustness of a system to such perturbations is called the stability radius. The concept of stability radii was introduced by Hinrichsen and Pritchard 1986 for timeinvariant differential or difference systems see 2 3 . It is defined as the smallest value p of the norm of real or complex perturbations destabilizing the system. If complex perturbations are allowed p is called the complex stability radius. If only real perturbations are considered the real radius is obtained. The computation of a stability radius is a subject which has attracted a lot of interest over recent decades see . 2 3 4 5 . For further considerations in abstract spaces see 6 and the references therein. Earlier results for time-varying systems can be found . in 1 7 . The most successful attempt for finding a formula of the stability radius was an elegant result given by Jacob 1 . In that paper it has been given by virtue of output-input operator a formula for Lp- stability for time-varying system subjected to additive structured perturbations of the form x t B