Finite Time Control For Uncertain TS Fuzzy System

The description and control problem of the complex nonlinear system has been one of the troubles in the realm of control theory all along. As an approach to describe and control the system,the fuzzy logic theory has been the common concerns of some researchers. This paper introduces the Takagi-Sugeno(TS) fuzzy model based modeling and controller design theory of the nonlinear system. And considering the factor of uncertainty which must be a in this premise, we studies the control problem of the system within the scope of finite time interval.Firstly, We study the finite time fragile control problem of the uncertain TS fuzzy systems with time-delay. By constructing Lyapunov-Krasovskii function and combining some new integral inequalities, a sufficient condition which guarantees that the closed-loop system is finite time stable. And the problem of solving the fragile controller is transformed into the feasibility problem of solving linear matrix inequality. Numerical examples demonstrated the promoted method is feasible, which has fully explained that the method has theoretical significance.Secondly, based on the finite time stable theory, we study the control problem of a class of TS fuzzy system with bounded external disturbance uncertainty. Designing state feedback controller which guarantees that the system is satisfied the finite time H_∞ performance, then we transform the problem of solving the controller into the feasibility of problem of solving linear matrix inequality. We solve the problem of poor performance and instability caused by the external disturbance for system. At last but not least, some numerical examples are provided to demonstrate the effectiveness of the results which was proposed.Then, considering the influence of time-delay, actuator saturation and finite time bounded on the system, we study the problem of finite time stable and bounded for the T-S fuzzy system with time-delay and input saturation. By giving the design method of memory state feedback controller, we consider the estimation problem of attraction domain for the closed-loop system. Some numerical examples are provided to demonstrate the effectiveness and merit of the proposed results.