Nonlinear Delay Systems Guaranteed Performance Analysis And H_ ¡Þ Robust Control

Uncertain nonlinear system with time-delays as a general system existing widely in the real world.In fact,nonlinearity exists commonly,and time-delay is inherently existing in general systems,and uncertainty is unavoidable in various practical control problem.Therefore,Researches on the control of uncertain nonlinear systems with time-delays have both theoretical and practical interest.Recently,singular system and neutral system are playing a more and more important role in practical control problems,thus they become the focus of many researchers.Many results of linear normal system have been generalized to singular system and neutral system one by one.Whereas,their complex mechanism make it difficult to research robust stability analyse and robust H_∞control.Praticularly,the study of robust stability analyse and robust H_∞control for them is on primary phase.At present,the research on the robust control theory is generally divided into two kinds:One aims to analyze and seek for the robust stability and stabilization, such as robust control theory.The other is the design of control according to the optimization of some kinds of performance index,such as the design of H_∞filter, guaranteed cost control theory and H_∞control theory.According to the known conclusion at the present time,this paper investigates the problems of garanteed cost control and H_∞control for nonlinear uncertain neutral system with time-delays, and guranteed cost control for nonlinear uncertain singular system with time-varing delay,based on the classical Lyapunov theory of stability,by application of the method of LMI(linear matrix inequality) and GA(genetic algorithm).The main conclusions in this paper are:(1) According to the results of nonlinear systems with time-delays and neutral systems with time-delays,attention is focused on the design of state feedback controllers such that the closed-loop systerm is asymptotically stable and the closed-loop cost function value is not more than a specified upper bound for all admissible uncertainty. One major contribution of the present work is that the solvability of design of nomemory state feedback controllers for a class of systems with(B+△B(t))f(·) nonlinear perturbations functions is easily obtained byφ-Procedure lemma.At last,the existence of suboptional nomemory state feedback guaranteed cost controller is derived in term of LMI.An example is used to illutrate the feasibility of the design procedure.(2) According to the results of nonlinear systems with time-delays and singular systems with time-delays,attention is focused on the design of guaranteed cost controller for nonlinear uncertain singular systems with time-varing delays.A new sufficient condition for the existence of suboptional guaranteed cost controller is established in terms of LMI.An example is used to illutrate the feasibility of the design procedure.(3)The problem of delay-dependent robust H_∞control is introduced for nonlinear neutral systems with time-varing delays.A new sufficient condition for robust H_∞controllers is derived in term of Lyapunov stability theory and GA.The method of design of suboptional robust H_∞controller for nonlinear uncertain neutral system with time-varing is obtained by the use of LMI,and two examples are used to illutrate the feasibility of the design procedure.