Control And Application Research Of 2-D Time-Delay Switched System Based On Roesser Model

Switching is an important phenomena in complex systems,so the stability and control problems of switched systems have been intensively researched over the past decades.In recent years,two-dimensions(2-D)switched systems have been used in many practical areas and have attracted extensive attention of scholars.Stability analysis of systems is an important topic,system stability is a prerequisite for a system to work properly,and it is well known that the Lyapunov function method is an effective analytical method for studying the stability of time-delay dependent switched systems.With the rapid development of industrial technology,the study of control for 2-D switched systems problems has received extensive attention,with both state feedback control and dynamic output feedback control being important methods.Control systems containing perturbations is also one of the key topics of research.Therefore,it is necessary and meaningful to analyze the stability and H∞ control problems of 2-D switched systems.In view of this,this paper considers exponential stability and finite region H∞ control problems for 2-D switched systems.The main research contents are as follows:Firstly,the finite-region stability for 2-D switched systems is investigated based on mode-dependent average dwell time(MDADT)method,the finite region is selected as a triangular region,which is more irregular than the square region in the previous study,and the sufficient condition to ensure the finite region stability of the system is obtained.For the case with H∞ perturbations,asynchronous phenomenon is produced due to time delay between state vector and controller mode,it is investigated that the asynchronous control problems with constant time-delay in the state vector,then a method designed of state feedback controller for closed-loop system with given H∞ performance is presented.If the time-delay in the state vector is zero,the verified results can be transformed into the existing results of the FMLSS model,indicating that the results proposed by us are more general.Secondly,the exponential stability problem of 2-D switched Takagi-Sugeno(T-S)fuzzy systems with stable and unstable subsystems is studied,considering the case of state systems containing constant time-delay.First applying the quasi-alternating switching criterion used in the study of switched systems,and specifying that the switching moment depends on i+j,fast and slow MDADT methods for stable and unstable subsystems are used respectively,then the stability criteria is obtained.Then a dynamic output feedback controller is designed to ensure the exponential stability of the system.And the feasibility and practical application value are verified by Matlab toolbox.Finally,the case of 2-D switched T-S fuzzy systems with time-varying delays is considered,then the Lyapunov-Krasovskii functional(LKF)is chosen.The sufficient conditions for the exponential stability of the system is obtained by using Jensen inequality and the Schur complementary lemma.In the study of 2-D switched T-S fuzzy systems,the case of time-varying delays is considered for the first time,and the results obtained are verified as feasible and applied to an example of a chemical reaction heat process.