H_∞Control For Singular Systems With Time-Delays

The singular system with time-delay is a class of time-delay systems broader thanothers. Singular systems have found in many practical applications, such as inengineering systems, manufacturing systems, population ecology systems, economicsystems, circuit network system, social systems and so on. Time delays are importantfactors which affect the performance of singular systems. The H_∞control by H_∞norm to describe can make the system has excellent performance. Therefore, theresearch for singular systems with time-delays has important theoretical and practicalsignificance.This dissertation studies the problem of H_∞control for singular systems withtime-delays by constructing appropriate Lyapunov-Krasovskii function, combiningwith integral inequality, singular value theory and linear matrix inequality (LMI)approach. The main works are as follows:Firstly, the mechanical system model is transformed into state equation. Theproblem of delay-dependent H_∞control for mechanical system is investigated by thesingular system theory. A sufficient condition is given to guarantees the mechanicalsystem is regular, impulse free, stable and satisfies the H_∞performance.Secondly, the problem of memory feedback non-fragile H_∞control for singularsystems with state-delay is dealt with. By constructing appropriate generalizedLyapunov-Krasovskii function, using Schur-complement Lemma and a new integralinequality, then a sufficient condition is given to guarantees the resultant closed-loopsystem is regular, impulse free, and stable with a H_∞norm bound constraint.Thirdly, the problem of delay-dependent robust H_∞control for time-delaysingular systems with saturating actuators and parameter uncertainties is investigated.Based on Lyapunov-Krasovskii stability theory, the design method of controller isgiven by the LMI method and the singular value theory.Finally, the problem of robust guaranteed cost H_∞control problem for a class ofsingular systems with multiple time delays subject to input saturation. Based on LMIapproach and the singular value theory, sufficient conditions for the existence of guaranteed cost H_∞control law and corresponding guaranteed cost performanceindex are obtained.