Robust Control For The Uncertain Nonlinear Singular Systems With State Time-delays

In singular systems, time delays, parameter uncertainties and nonlinear disturbancesare widespread in the practical application system, which affects the good performanceand stability of the singular systems. For singular systems robust control theory researchhas always been the hot spot of the control theory, challenging and necessity. Now therobust control and guaranteed cost control can make the singular system with goodperformance,Therefore, studying the delay-dependent (linear and nonlinear) of uncertainsingular systems robust H control and guaranteed cost control problem has importantapplication value. In this paper, we study a class of input delay and uncertain linear andnonlinear singular systems with state delay robust control and guaranteed cost controlmethod for the design of the controller.The paper studies a class of input delay and linear uncertain singular systems withstate delay and a class of contains input delay and nonlinear uncertain singular systemswith state delay.By using Lyapunov function,the control theory,linear matrix inequality,fundamental inequality and scchur lemma, controller’s design method is optimal.The paper studies a class of input delay and state time delay linear uncertain singularsystems and nonlinear systems with state delays guaranteed cost control problem ofuncertain singular systems. Combining with the Lyapunov stability theory, the quadraticperformance index and related lemma, a memoryless state feedback controller is designed,and the closed-loop system is stable and the performance index of the closed-loop systemis not greater than the upper bound index.The paper studies a class of markov jump nonlinear uncertain singular time-delaysystems robust control problem. The strict LMI conditions, based on Lyapunov function,by using the linear matrix inequality method, the basic inequality and scchur lemma, tosolve the uncertain delay dependent stability problem and the use of LMI toolbox meet thestate of the system controller is designed.