离散T-S模糊双线性随机系统的模糊观测器控制

Observer-based Fuzzy Control Design for Discrete-Time T-S Fuzzy Bilinear Stochastic Systems

本文基于分段二次李雅普诺夫函数(PQLF)稳定性理论,研究了一类受随机干扰的离散T-S模糊双线性系统的随机均方稳定控制问题。在系统状态不完全可测的情况下,通过设计基于模糊双线性观测器的控制器,使闭环增益双线性系统随机均方稳定,利用Schur补引理给出了保守性较小的随机均方稳定的充分性条件。观测器的设计可以通过序列线性规划矩阵方法(SLPMM)求解得到。数值例子验证了该设计方法的有效性。

This paper is concerned with the problem of observer-based fuzzy control design for discrete-time T-S fuzzy bilinear stochastic systems. Based on the piecewise quadratic Lyapunov function（PQLF）,the fuzzy observer-based controllers are designed for T-S fuzzy bilinear stochastic systems. It is shown that the stability in the mean square for discrete T-S fuzzy bilinear stochastic systems can be established if there exists a set of PQLF which can be constructed and the fuzzy observer-based controller can be obtained by solving a set of nonlinear minimization problem involving linear matrix inequalities （LMIs） constraints. An iterative algorithm making use of sequential linear programming matrix method （SLPMM） to derive a single-step LMI condition for fuzzy observer-based control design. Finally, an illustrative example is provided to demonstrate the effectiveness of the results proposed in this paper.