Analysis And Control For Fuzzy Stochastic Systems Based On T-S Models

As a control method is different from traditional control theory, fuzzy control can make full use of the experience and knowledge of the experts, and has the advantage of considerable robustness for nonlinear, time-varying and delay systems’control. During recent studies, a systematic framework of Takagi-Sugeno (T-S) fuzzy model study is formed to deal with complex nonlinear system’s stability analysis and synthesis problems, and in this model there are lots of research about stability on all kinds of fuzzy-stochastic systems and robust control. However, the stability conditions and control of T-S fuzzy systems based on quadratic Lyapunov function are quite conservative. On base of Lyapunov control theory and linear matrix inequality approach, a class of LMI conditions is proposed, which make the stochastic T-S fuzzy systems exponentially stable in mean square. In addition, we reaserch the problems of state feedback control on the basis of parallel distributed compensation approach.Firstly, the dissertation gives a common mathematic model of an uncertain fuzzy stochastic time-delay system by using a combination of T-S fuzzy system, stochastic differential equation, random factor, time-delay state and uncertain parameter. And then, some important concepts of system stability and the Lyapunov stability theorems are given.Secondly, as for this model, by taking full account of delay information, constructing a suitable Lyapunov-Krasovskii functional, using the Jensen integral inequality and free weighting matrices, conditions of stability of this system and fuzzy controller designing method are given in the form of linear matrix inequality (LMI) under delay-dependent conditions. Gradually, the nominal system stability analysis is firstly considered, and then make further analysis to the system according to affect of uncertainties and time-delay factors; further, on the basis of the robust stability analysis, the robust control problem for non-linear fuzzy stochastic systems is studied, using the PDC method to design the fuzzy controller, and further considering the feedback delay situation. The controller is designed for all admissible uncertainties conditions, that is robust control.Finally, the conclusions and outlook is given, then the contribution of this paper and further research directions are pointed out.By the analysis of the Lyapunov function, this paper give full consideration of the relationship of the current condition, time-delay state, boundary delay state and the state x(t). Based on Jensen integral inequality, neither model transformations nor bounding techniques for cross terms are employed, so the derived criterion is less conservative than the most existing results. The stability condition is applicable not only to the condition x(t)<1, but also is satisfied when the delay variation rate is greater than1, the result is available for a wide range by use the free weighting matrices method. A series of examples in the paper show that, the delay-dependent condition is effective and feasible, and the obtained results are less conservation.