The Study Of Stability And Guaranteed Cost Control For The Singular Systems Based On LMI Approach

The stability and stabilization problem of singular systems or singular systems withtime-delay is one of the fundamental problems in the theory of singular system. The studyof them is much more complicated than that of state-space systems because the singularsystem requires considering not only stability, but also regularity and causality (for discretesingular systems) or impulse immunity (for continuous singular systems).Recent years, the linear matrix inequality (LMI) approach has been attracting moreand more attention due to its extensive applications in solving various control problems.However, the problem of stability of large-scale singular systems with time-delay via LMIapproach is scarcely reported in the literatures.On the basis of the recent progress on singular systems models, this dissertationimplements a systematic study on the stability, stabilization and guaranteed cost control ofsingular systems with time-delay models and parameter uncertainty. By means of LMItechniques, the main results obtained in this dissertation are as follows:â…°) The problem of stability and stabilization of singular systems is investigated.Some stabilization controllers are proposed for singular systems. The problems of robuststability and robust stabilization of singular systems with parameter uncertainties areinvestigated via linear matrix inequality (LMI) method. A theorem of robust stability ofsingular systems with parameter uncertainties is obtained and the robust stabilizationcontrollers are proposed.â…±) The problems of stability and stabilization of the continuous singular systemswith delay-time and the singular linear large-scale system with delay-time are studied. Thecorresponding theorems of stability are presented, based on which the stabilizationcontrollers are designed.â…²) The problems of robust stability and robust stabilization of continuous singularsystems with delay-time and parameter uncertainties & singular linear large-scale systemwith delay-time and parameter uncertainties are discussed. The corresponding theoremsand controllers of robust stability are presented.â…³) For a class of singular large scale systems with value bounded parameteruncertainty and a quadratic cost index, the problem of designing an optimal guaranteed cost state feedback controller is considered. A sufficient condition for the existence of theoptimal guaranteed cost controller and the design of optimal guaranteed cost controllers arederived. Moreover, the problem of guaranteed cost state feedback controller design issurveyed. A sufficient condition for the existence of the guaranteed cost controller and thedesign of guaranteed cost controllers are derived.