Research On Robust Stability, Passivity Of Impulsive Systems And Impulsive Control

It is well known that impulsive effects are common phenomena in manyevolutionary systems.The stability and control performance may change fornonlinear dynamic systems with impulsive effects,so the studies on impulsivesystems and impulsive control have important theoretical meaning and practicalvalues,which have been widely considered by many researchers.The main content of this dissertation include:(1) Research on robust stability,robust control,passivity and passification of uncertain impulsive dynamic systems;(2) Fuzzy modeling and its impulsive control for chaotic systems;(3) Research onimpulsive synchronization for chaotic systems;(4) Research on impulsive controlfor Takagi-Sugeno (T-S) fuzzy systems.The main originality in this paper can be summarized as follows:1.Research on robust stability and passivity for uncertain T-S fuzzysystems with impulsive effectsUncertainties often occur in mathematical modeling.And there exist a lot ofresults for passivity of nonlinear systems.However,for systems with uncertaintiesand impulsive effects,there are few publications on the problems of passivity andpassification.We study robust stability,robust H∞control,passivity andpassification for T-S systems with uncertainties and impulsive effects.Some robuststability and passivity criteria are given in terms of linear matrix inequalities (LMIs).Using parallel distributed compensation (PDC) technique,fuzzy controllers aredesigned for robust H∞control and passification of uncertain T-S fuzzy systemswith impulsive effects.2.Research on fuzzy modeling and its impulsive control for chaoticsystemsChaos may change the stability and control performance of complex nonlinearsystems.However,a chaotic system is stabilizable via impulsive control.Based onT-S fuzzy model,comparison principle and LMIs,we study the stability of chaoticsystems via impulsive control.Sufficient conditions are given in terms of LMIs,and the design procedure of impulsive controller is proposed.We also discuss itsapplications to various chaotic systems.3.Research on synchronization of chaotic systems via impulsive controlIt is important for secure communications to study the chaotic synchronizationdue to the inscrutability of the chaotic system.It is pointed out that impulsivecontrol can give better performance than continuous control.Based on T-S fuzzymodel and LMI technique,impulsive controllers have been designed forsynchronizing chaotic systems.4.Research on impulsive control for T-S fuzzy systemsComplex nonlinear systems can usually be represented with T-S fuzzy modelon certain domain.First,we study the exponential stabilization for a class ofdiscrete-time T-S fuzzy systems via impulsive control.Then,based on Lyapunovfunctionals,a novel impulsive stabilization scheme is proposed for continuous-timeT-S fuzzy systems with time-delay.