Robust Stability Of A Class Of Discrete 2-D Switched Systems

In recent years,with the rapid development of society,multidimensional systems,switching systems,especially discrete two-dimensional(2-D)switching systems,have been more and more widely used in important fields such as smart transportation,digital filtering and so on.The first problem in the control system is to ensure its stability.Therefore,it is important to study the stability problems related to 2-D switching systems and the design of the system controller.However,most of the studies on 2-D switching systems are focused on fixed system models.Considering that the actual project is often affected by the internal and external environment,which makes the system itself have some uncertain parameters,this paper mainly takes the discrete 2-D switching system with norm-bounded uncertainty as the research object,and focuses on the robust stability of the system.The main content of the study is the following three parts:(1)The first part mainly studies the robust asymptotic stability of discrete 2-D switching systems with norm-bounded uncertainty under any switching conditions based on FM models.Based on the idea of common Lyapunov function,the asymptotic stability of open-loop system and H? performance index of the system are studied by constructing appropriate Lyapunov function,and a state feedback controller is designed for closed-loop system design.Then the multiple Lyapunov function method is used to study that the system has the same performance indicators and sufficient conditions to be met,and the latter method is proved to be less conservative than the former..(2)Considering the harsh conditions of arbitrary switching,which also leads to large conservativeness of the obtained results.Therefore,the second part focuses on the robust exponential stability of discrete 2-D switching systems with norm-bounded uncertainty based on the Roesser model with constraints.Based on the idea of average dwell time,an exponential stability criterion for robust H? performance index of open-loop 2-D switching system is obtained by constructing an appropriate Lyapunov function and rigorous theoretical derivation.On this basis,the design steps of the dynamic output feedback controller of the closed-loop system are further given.(3)Considering the existence of delay in real life,the third part focuses on discrete2-D switching systems with norm-bounded uncertainty based on FM constant-time-delay model.The robust stability of the system under constrained switching conditions is studied.Based on the idea of average dwell time,by constructing an appropriate Lyapunov-Krasovskii functional,an exponential stability criterion for robust H?performance index of the open-loop 2-D switching system is derived,and a state feedback controller is designed for the closed-loop system.The above criteria are given in the form of matrix inequality,and their feasibility is verified by numerical examples.