Analysis And Control Of Continuous T-S Fuzzy Systems:Augmented LKF Approaches

Due to the nonlinear Feature of many practical dynamic systems and the universal nonlinear approximation ability of Takagi-Sugeno(T-S)fuzzy models,researchers have conducted a lot of research on the modeling,analysis and synthesis of T-S fuzzy modelbased nonlinear systems and have achieved fruitful results.In several practical systems,the time-delay phenomenon is inevitably encountered in the state,control input or measurement,and and appears in either constant,time-varying or random way,which cause system performance degradation or even.It is well-motivated to study the effect of time-delay on the stability of the T-S fuzzy system and what kind of time-delay the system can be tolerated.At present,the delay-dependent stability results of T-S fuzzy systems with time-varying delays are sufficient conditions.There is still much room to achieve some improved approaches of searching for the maximum allowable delay bound while ensuring the stability of fuzzy delay systems by making full use of information on time-varying delay.Along with the increasing complexity of modern industrial systems and the rapid development of digital information technology,digital equipment must sample the signals before processing the signals generated by each sensor.Early studies on fuzzy sampleddata control for nonlinear systems usually assume that continuous plants and sampled-data controllers share the same continuous premise variables to ensure the synchronous running of the plants and the controllers.However,the sampled-data controller can only acquire discrete-time data information in a digital control environment,which certainly leads to the closed-loop model in the form of an asynchronous T-S fuzzy system.By utilizing the information of sampling interval and exploiting the asynchronous running characteristics between the fuzzy plant and the sampled-data controller,the analysis and synthesis of T-S fuzzy sampled-data control system has become a hot topic in the control area.Based on the above analysis,this paper constructs some novel augmented lyapunovkrasovskii functional(LKFs)to deal with the problem of stability analysis and synthesis of a class of T-S fuzzy systems with state delay and the problem of asynchronous control design of a class of T-S fuzzy sampled-data systems,respectively.The research content and results of this paper mainly include the following two aspects:(1)For T-S fuzzy systems with constant and time-varying delay,some novel augmented LKFs are constructed based on the form of Bessel-Legendre(B-L)inequality,and some delay-dependent stability conditions with less conservatism are established.In particular,some relaxation matrix variables are introduced by applying the B-L inequality,and the positive definiteness of the constructed LKF and the negative definiteness of its derivative are proved in time-varying delay case.case.Further,the delay-derivative-dependent stability conditions are obtained.Then,the design results of a fuzzy controller with less conservatism are given in the form of linear matrix inequality.Two examples are given to illustrate the effectiveness and advantage of the proposed conditions.(2)Considering the continuous T-S fuzzy model and fuzzy sampled-data controller,the closed-loop system is modeled as an asynchronous T-S fuzzy system,in which the fuzzy plant uses continuous-time premise variables and membership functions,but the sampleddata controller receives the corresponding discrete-time data.A novel augmented fuzzy looped-LKF related to sampling time is constructed by taking the state information of endpoints on both sides of the control actuation interval into account and using the form of affine B-L inequality,and the stability condition that depends the sampled-data interval is derived by the LKF.The existence condition of the asynchronous controller is obtained by linear matrix inequality.Two numerical examples are given to prove that the condition can obtain the maximum allowable sampling period while ensuring stability of the closed-loop system.Compared with the existing results,this paper proves the superiority of the conditions are confirmed.Finally,the research work of this paper is summarized,and the future research directions are prospected based on the current work.