Dynamic Output Feedback Controller And Fault Detection Filter Design For Positive T-S Fuzzy Systems With Delays

With the development and wide application of fuzzy control theory, the stability and con-trollers design problems of general T-S fuzzy systems have attracted a lot of attention. Because of the design of dynamic output feedback controller is complicated, experts both domestic and abroad have done a lot of research work. However, there exist a class of fuzzy system which must be nonnegative in practical engineering. So the corresponding dynamic systems must be described by positive T-S fuzzy systems. But up to now, there is few work on positive T-S fuzzy system with delays, therefore this paper deals with the problem of designing dynamic output feedback controller and fault detection filter design for positive T-S fuzzy systems with delays. The main works of this paper are given as follows:1) The problem of designing dynamic output feedback controllers for discrete-time positive T-S fuzzy systems with delays is investigated. Firstly, by using the Schur complement lemma, a sufficient condition of the asymptotic stability for discrete-time positive T-S fuzzy systems with delays is given in terms of matrix inequalities. Then, based on the stability conclusion,the specific design method of dynamic output feedback controllers for discrete-time positive T-S fuzzy systems with delays is obtained. At last, a numerical example is given to show the effectiveness of the proposed method.2) The problem of designing dynamic output feedback controllers for continuous-time posi-tive T-S fuzzy systems with delays is investigated. Firstly, a sufficient condition of the asymptotic stability for continuous-time positive T-S fuzzy systems with delays is given in terms of matrix inequalities on the existing conclusions. Then, based on the stability conclusion and consid-ered the positive property of systems,the specific design method of dynamic output feedback controllers for continuous-time positive T-S fuzzy systems with delays is obtained. At last, a numerical example is given to show the effectiveness of the proposed method. 3) The problem of designing mixed L_/L1fault detection filter for the discrete-time positive T-S fuzzy systems with time-varying delays is investigated. Firstly, a new sensitivity measure of the residual signal to faults, called L_index,is for the first time proposed. By using the linear copositive Lyapunov-Krasovskii function, a sufficient condition is given to ensure the system is asymptotically stable. Then based on the stability conclusion,we obtain the sufficient conditions to guarantee the existence of theî–¥fault detection filter and L_/L1fault detection filter for the discrete-time positive T-S fuzzy systems with time-varying delays. Then the specific design methods are proposed in terms of linear programming. At last, a numerical example is given to show the effectiveness of the proposed method.