Sampling-Fuzzy-Dependent LKF for T-S Fuzzy Systems Under Sampled-Data Control

This article focuses on the stability analysis and stabilization design of Takagi–Sugeno (T-S) fuzzy systems under sampled-data control. First, by capturing the constant characteristic of the sampling time in the sampling interval, a novel sampling-fuzzy-dependent Lyapunov–Krasovskii functional (LKF) is proposed, which can introduce both fuzzy-dependent and sampling-dependent information and avoid the derivatives of membership functions (MFs). Second, a novel synchronization method via the slack membership-dependent matrices is proposed to synchronize the mismatched MFs between the plant and controller, which can overcome the limitations that the MFs must be greater than zero in existing works. Thus, improved stability and stabilization conditions are obtained. Finally, two case studies are given to show the effectiveness and merits of the proposed methods.