Stability And Robust Stability Analysis Of A Class Of Generalized Systems

The asymptotic stability and stabilization are the fundamental research problems in the large-scale singular systems. Because of the particularity of singular system, the research on its asymptotic stability needs to consider not only stability but also regularity, and the research on its robust stability needs to consider not only stability and regularity but also impulse (for continuous time case) or causality (for discrete time case), as regularity and impulse of singular system are all susceptible to the parameter uncertainties. The large-scale singular systems are difficult to be centralized controlled due to their enormous dimensions, multitudinous elements and busy information changes between subsystems, so it is common to adopt decentralized control for a large-scale singular system.This paper researches the stability and the robust stability of continuous large-scale singular system, and the parameter regions to maintain the singular system robust stable. The main results are as follows:(1) By means of Lyapunov approach the stability of large-scale singular system is investigated, and the sufficient conditions are obtained under the conditions that all of the isolated subsystems are regularity and asymptotic stable.(2) The robust stabilization for large-scale singular system with uncertainties satisfying generalized matching conditions is discussed, and the state feedback controller is designed, such that the closed-loop large-scale singular system is robust stable.(3) For singular system with a type of polytope uncertainties, parameter regions to maintain such system robust stable are obtained, and the feedback controller to keep closed-loop system robust stable is designed.