Regional Output-Feedback Control for T–S Fuzzy Systems Using Lyapunov Functions With Polynomial Dependency on States and Membership Functions
针对连续时间T-S模糊系统，提出一种新的李雅普诺夫函数，其多项式依赖状态和隶属度函数，结合迭代LMI算法设计输出反馈控制器，无需隶属度导数界，能扩大吸引域并提高收敛速度。
This article addresses the problem of local output-feedback control design for continuous-time Takagi–Sugeno fuzzy systems using the parallel distributed compensation (PDC) approach. The main contribution is the introduction of a novel class of Lyapunov functions with polynomial dependence on both the system states and the membership functions (MFs), providing less conservative stability and synthesis conditions. To compute the PDC gains, a locally convergent iterative algorithm based on linear matrix inequalities (LMIs) is proposed. Unlike many existing methods, the approach eliminates the need for bounds on the time derivatives of MFs by explicitly incorporating their dynamics into the stability conditions. The algorithm operates in two phases: first, optimizing the decay rate of the closed-loop trajectories, andsecond, maximizing the estimated domain of attraction (DOA) under a fixed decay rate. Comparative numerical examples based on benchmark systems demonstrate the superior performance of the proposed method over existing techniques, particularly as the polynomial degree of the Lyapunov function increases.