Stability Analysis And Control Design For Discrete-time 2-D Switched Systems

As one of important research directions of hybrid systems and 2-D systems,2-D switched systems have been applied in many engineering areas,such as power trans-mission and thermal process in pipe furnaces.Since 2-D switched systems posses both complex dynamics of switched systems and the inner coupling structure of 2-D systems,the problems of stability analysis and control synthesis are interesting and challeng-ing.Based on the basic concepts and methods of the control theory,by using common Lyapunov functions and multiple Lyapunov functions,Lyapunov-Krasovskii functional technique and average dwell time method,the stability analysis and control design are concerned in this paper,the effective control strategy and the novel stability criteria are proposed,and a series of well-established,systematical and important results are obtained.The main results of the dissertation are summarized in the following:1.The H? control problem under arbitrary switching law for a class of discrete-time 2-D switched systems represented by a model of Roesser type is investigated.Sufficient conditions for the asymptotical stability and H? disturbance attenuation performance of the underlying system are derived via common Lyapunov function ap-proach and multiple Lyapunov function approach respectively.Then,based on the obtained stability results,two state feedback H? controller design methods are pro-posed.Since the strict requirement on the existence of a common quadratic Lyapunov function for various subsystems brings conservatism.Multiple Lyapunov function ap-proach is a strong tool in studying switched systems,through which the obtained result leads to less conservatism.2.The weighted H? control problem for a class of discrete-time 2-D switched systems represented by a FM LSS(Fornasini-Marchesini local state space)model is considered.Sufficient conditions for the exponential stability and H? disturbance attenuation performance of the underlying system are derived in terms of LMI via an appropriate Lyapunov function and average dwell time approach.Then,dynamic output feedback controller is proposed to guarantee that the resulting closed-loop system is exponentially stable and has a prescribed H? performance level.3.The problem of delay-dependent H? control for 2-D switched discrete state delay systems described by FM LSS model is concerned.Sufficient conditions for exponential stability and weighted H? disturbance attenuation performance of the underlying system are derived in terms of LMI via a new Lyapunov-Krasovskii func-tion,time dependent analysis and the average dwell time approach.Based on the obtained results,a state feedback controller design is proposed to guarantee that the resulting closed-loop system is exponential stable and achieves a prescribed disturbance attenuation level.4.The problem of exponential stabilization for a class of positive 2-D switched delay systems described by the Roesser model is addressed.Delay-dependent sufficient conditions for exponential stability of positive 2-D switched systems with state delays are given in terms of LMI via an appropriate co-positive Lyapunov-Krasovskii function and average dwell time method.Furthermore,the design of positive state feedback controller under which the closed-loop system meets the requirement of positivity and exponential stability is presented.5.The state feedback control problem is concerned for a class of 2-D discrete-time stochastic systems with time-delays,randomly occurring uncertainties and nonlinear-ities.Both sector-like nonlinearities and the norm-bounded uncertainties enter into the system in random ways,and such randomly occurring uncertainties and nonlin-earities obey certain mutually uncorrelated Bernoulli random binary distribution laws.Sufficient computationally tractable conditions are established for the 2-D nonlinear stochastic time-delayed systems to be asymptotically stable in the mean-square sense,and then the explicit expression of the desired state feedback controller gains is derived.