Aperiodic-Sampled-Data-Based Robust H_∞ Control For Several Classes Of T-S Fuzzy Systems

In recent years,fuzzy control of nonlinear systems has been paid more and more attention.In particular,takagi-Sugeno（T-S）fuzzy model is widely used,which can accurately represent many chaotic systems,and then analyze and synthesize a highly complex chaotic system systematically by using the existing linear system theory.In this paper,the T-S fuzzy system is discussed.Based on theH_∞performance,many problems such as aperiodic sampling control,state feedback control and input saturation control are studied.The specific research contents are as follows:1.For a class of T-S fuzzy systems based on aperiodic sampling,theH_∞performance is analyzed and the design of state feedback controller is studied.In order to make full use of system information,a new lyapunov functional composed of closed-loop functions is constructed.On the basis of the functional,the stability conditions with less conservatism are given in the form of linear matrix inequalities.At the same time,a state feedback controller is proposed to ensure the stability of the system under the condition ofH_∞performance.The results show that the method is effective.2.For a class of T-S fuzzy systems based on input saturation,theH_∞performance is analyzed,and the design of non-periodic sampling state feedback controller is studied.In order to make full use of the information from(₆))to（）and（）to(₆+1)),we construct a novel Lyapunov function,which consists of a bilateral closed-loop function.On the basis of this function,the stability condition with less conservative is given in the form of linear matrix inequality,and a controller is given to make the system stable.At the same time,the optimization condition is given in the form of linear matrix inequality to estimate the range of attraction domain under input saturation condition.The results show that the method is effective.3.For a class of T-S fuzzy systems based on Markov jump parameters,theH_∞performance is analyzed and the design of state feedback controller is studied.Firstly,in order to make full use of the system information,a new modal dependent Lyapunov function composed of closed-loop functions is constructed.On the basis of this function,the stability conditions with less conservatism are given in the form of linear matrix inequalities.At the same time,a design algorithm of state feedback controller for the studied T-S fuzzy system is proposed to ensure the stability of the system under the condition ofH_∞performance.The results show that the method is effective.