Research On Robust Control For The Uncertain Generalized Systems With Multiple Time-varying Delay

The time delay, nonlinear characteristics and uncertainties are common exist inpractical control systems, which affect the good performance and stability of generalizedsystems. This made them become three main factors which must be considered in controlsystem study. In recent years, the robust control question for generalized systems withuncertainties has been one of the hot topics in the study of control theory. Althoughresearches of time-delay systems have been achieved perfect results, studies for uncertainsingular systems with multiple time-varying delays are very few. Nonlinear perturbation isexist in most uncertain generalized systems. So the study of uncertain generalized systemswith multiple time-varying delay with nonlinear perturbations has an important theoreticalsignificance and practical value. Based on the analyze, research, absorbing for the existingachievements of domestic and foreign, the article focuses on the robust control problem ofuncertain generalized systems with multiple time-varying delay. The robust stabilityproblem and robust passive control are discussed and get a very good conclusion.The paper, at first, the basic knowledge about research is briefly introduced. Then therobust control problems for a class uncertain generalized systems with multipletime-varying delay are discussed. For such a generalized system, we firstly study therobust stability of generalized systems with time-varying delay. Starting from the basictheoretical knowledge, the Lyapunov function is given. And relevant lemma, controltheory, and LMI method was used. A condition which not relies on delay of robustasymptotic stability for the system is derived.The paper, further, dicusses the robust control problems of uncertain generalizedsystems with multiple time-varying delay. Based on the researches, the paper getsasymptotically stable and sufficient conditions. In the process, the Schur and relevantlemma, and stability theory are used. At the end of research, the feasibility and efficiencyof the conditions were verified by numerical simulation.Finally, the robust passive control of uncertain generalized systems with multipletime-varying delay is studied. Based on Lyapunov function, used the Jensen inequalitysimplified integral term in derivation process, a passive condition of generalized systems is got. Based on LMI methods, the paper integral form of Lyapunov function is chosen.Furthermore,the design of a memoryless feedback controller is obtained in terms of thesolution of LMI, making the closed-loop system strictly passive. Finally, the feasibilityand efficiency of the method are verified by number simulation, which is conductedthrough the LMI toolbox in Matlab.