Robust Control And Filtering For Discrete-time Switched Systems With Persistent Dwell-Time

Switched systems have attracted considerable attention from researchers with dif-ferent backgrounds,such as computer science,applied mathematics,and control science,due to their advantages in system modeling and potential for practical application.Most of the current research results on switched systems are concentrated in the field of 1-D switched systems,and the switching signals considered focus on dwell-time and aver-age dwell-time.At the same time,there are relatively few research results on persistent dwell-time which is more general and more flexible.On the other hand,switching phe-nomena are also widespread in 2-D systems of practical projects,such as multi-channel power transmission systems,thermal reaction processes in chemical containers,etc.2-D switched system combines the structural complexity of 2-D system with the complex dynamic behavior caused by the switching signal.The research on this kind of system is not only of great theoretical significance and practical value but also of great challenge.Based on previous research,this thesis systematically investigates the problems of stability analysis,controller and filter design of 1-D and 2-D discrete-time switched systems with persistent dwell-time and mode-dependent persistent dwell-time.Firstly,the stability problems of 1-D and 2-D discrete-time switched systems subject to persistent dwell-time and mode-dependent persistent dwell-time are studied.Based on the quasi-time-dependent switched Lyapunov function,the revised stability criteria for 1-D discrete-time switched systems with mode-dependent persistent dwell-time are proposed.Further,based on the quasi-time-dependent 2-D switched Lyapunov functions,the sufficient conditions for the exponential stability of 2-D discrete-time switched systems subject to persistent dwell-time and mode-dependent persistent dwell-time are established,which provides a theoretical foundation for the design of controller and filter for such systems.Secondly,robust H_∞static output feedback control problem subject to mode-dependent persistent dwell-time is studied for 1-D discrete-time switched systems with time-varying and polytopic uncertainties.A quasi-time-dependent and parameter-dependent switched Lyapunov-like function is proposed.The revised multiple Lyapunov-like functions not only depend on the uncertain parameters but also extends it to a quasi-time-dependent form by constructing a schedule suitable for mode-dependent per-sistent dwell-time switching signals.Robust H_∞static output feedback controllers under two different cases are designed for uncertain 1-D discrete-time switched systems by us-ing the improved multiple Lyapunov-like functions,and a non-weighted H_∞disturbance attenuation performance is given.Thirdly,the state feedback control problem of 2-D discrete-time switched systems with persistent dwell-time is studied.Based on the quasi-time-dependent 2-D switched Lyapunov function,the state feedback controller is designed for 2-D discrete-time switched system without external disturbance to ensure the closed-loop system is exponentially stable.On this basis,further considering the case where there are external disturbances in the subsystems,a weighted H_∞disturbance attenuation performance is given,and the quasi-time-dependent H_∞state feedback controllers are designed.Then,the static output feedback control problem of 2-D discrete-time switched systems with mode-dependent persistent dwell-time is studied.Aiming at the situation that the disturbance can be ignored,a static output feedback controller design method to ensure the exponential stability of the closed-loop system is proposed based on the quasi-time-dependent 2-D switched Lyapunov function.On this basis,further considering the case of the existence of disturbances in subsystems,the sufficient conditions for the existence of quasi-time-dependent H_∞static output feedback controllers for 2-D discrete-time switched systems are presented.Finally,quasi-time-dependent H_∞filtering approach to 2-D discrete-time switched systems with mode-dependent persistent dwell-time is studied.Based on the quasi-time-dependent 2-D switched Lyapunov-like function,a criterion for exponential stability of the filtering error system is presented,and a weighted H_∞disturbance attenuation performance is given.On this basis,sufficient conditions for the existence of quasi-time-dependent H_∞full-order filters are established.Time-independent filters can be a special case of quasi-time-dependent filters,indicating that the quasi-time-dependent filter design method is less conservative.