Event-triggered Control,Filtering And Singular Dynamic Analysis For Switched Linear Systems

Based on the recent research on the theory of switched systems,networked control methods and the theory of descriptor systems,this dissertation investigates the analysis and design problem for switched systems and several new results are obtained.The main results in this dissertation are as follows:Firstly,the event-triggered H? filtering problems for both continuous-time and discrete-time linear switched systems are investigated.Based on merged switching signals,by using average dwell time methods and constructing quadratic Lyapunov functions,sufficient con-*ditions for exponential stability of filtering error systems are obtained,which also guarantee the suitable weighted H? performance.Furthermore,linear matrix inequality based design schemes for H? filters are presented.Secondly,the event-triggered stabilization problems for both continuous time and dis-crete time linear switched systems are discussed.New switching signals are obtained by combining switched signals with sampling signals at event triggered transmission instants.Based on new switching signals,the sampled-data control closed loop systems in the continuous-time case and the closed loop systems with network transmission delay in the discrete-time are modeled as switched systems with state delay,respectively.Using average dwell time methods and constructing quadratic Lyapunov functionals with mode and time delay depen-dence,time-delay dependent sufficient conditions for exponential stability of closed loop systems are derived,and linear matrix inequality based design methods of stabilizing con-troller are proposed.Thirdly,for both continuous-time case and discrete-time case,the event-triggered H?control of linear switched systems is investigated.Based on merged switching signals,con-trol closed loop systems are modeled as switched systems with state delay.Using average dwell time methods and multiple Lyapunov functional techniques,time-delay dependent suf-ficient conditions are obtained such that the closed loop system is exponentially stable and satisfies suitable weighted H? performance.In addition,linear matrix inequality based de-sign schemes for the H? controller are proposed.Then,the stability analysis problem for linear continuous-time Markovian switching singular systems is addressed.Based on a refined description for jumps of the system states at the switching instants,sufficient conditions,and necessary and sufficient conditions for exponential stability in the mean-square sense of the Markovian switching singular system are obtained by means of multiple Lyapunov function methods when the state transition matrix is completely known.The obtained results present a new analysis of the impact for switching law-induced state jump on the stability property of the considered system.Fur-thermore,when the state transition matrix is partially unknown,new sufficient conditions for exponential stability in the mean-square sense of the Markovian switching singular system are derived based on the necessary and sufficient conditions obtained.Finally,stabilization of switched linear singular systems with state reset and its appli-cations are investigated.Firstly,based on the reported results on switched singular systems,the state reset model for switched singular systems is proposed.When all subsystem is regular,impulse-free and stable,a sufficient condition of stability for the switched singular system with pre-specified state reset is obtained.Then,the stabilization problem by state resetting is investigated and algorithm for computing the reset matrices is presented.Sec-ondly,the detection and stabilization problems for linear singular systems are addressed.It is assumed that the decoder-estimator and decoder-controller can only receive the transmitted sequence of finite coded signals via a limited digital communication channel with missing measurements.Coder-decoder procedures for detection and stabilization of the continuous-time singular systems are proposed,in which the compensation term is introduced to meet the compatible requirement.Sufficient conditions of detectability and stabilization involving the parameter of quantizer,the sampling period and data packet dropout rate are obtained.