Fuzzy Static Output Control of T-S Fuzzy Stochastic Systems via Line Integral Lyapunov Function

Processes

Cheung-Chieh Ku¹  Yann-Hong Lin¹  Yu-Yen Hsieh¹  Yun-Chen Yeh¹ 

[1] Department of Marine Engineering, National Taiwan Ocean University, Keelung 202, Taiwan;

关键词: T–S fuzzy systems;    static output control;    stochastic system;    line-integral Lyapunov function;    projection lemma;   

DOI  :  10.3390/pr9040697

来源: DOAJ

【 摘 要 】

Considering some unmeasurable states, a fuzzy static output control problem of nonlinear stochastic systems is discussed in this paper. Based on a modelling approach, a Takagi–Sugeno (T–S) fuzzy system, constructed by a family of stochastic differential equations and membership functions, is applied to represent nonlinear stochastic systems. Parallel distributed compensation (PDC) technology is used to construct the static output controller. A line-integral Lyapunov function (LILF) is used to derive some sufficient conditions for guaranteeing the asymptotical stability in the mean square. From the LILF, a potential conservatism produced by the derivative of the membership function is eliminated to increase the relaxation of sufficient conditions. Furthermore, those conditions are transferred into linear matrix inequality (LMI) form via projection lemma. According to the convex optimization algorithm, the feasible solutions are directly obtained to establish the static output fuzzy controller. Finally, a numerical example is applied to demonstrate the effectiveness and usefulness of the proposed design method.

【 授权许可】

Unknown