Dissipativity Analysis for T-S Fuzzy System Under Memory Sampled-Data Control

The dissipative stability problem for a class of Takagi-Sugeno (T-S) fuzzy systems with variable sampling control is the focus of this paper. The controller signals are assumed to transmit with a constant delay. Our aim is to design the sampled-data controller such that the T-S fuzzy system is globally asymptotically stable with a $(\mathcal {Q},\mathcal {S},\mathcal {R})$ - $\gamma $ -dissipative performance index. The stability is analyzed by using a novel piecewise Lyapunov-Krasovskii functional (LKF) together with a looped-functional and free-matrix-based (FMB) inequality method. First, several useful linear matrix inequality (LMI) conditions are derived to verify the dissipative stability of the T-S fuzzy system and then the controller gains matrices are expressed by resorting the LMI approach with the maximal-allowable upper bound (MAUB) of sampling periods. The proposed LMI conditions can be easily solved by using the MATLAB tool box. Finally, the numerical example of a truck-trailer system is considered and analyzed by the proposed scheme to illustrate the benefit and superiority.

Automated summary

This paper focuses on the dissipative stability problem for a class of Takagi-Sugeno (T-S) fuzzy systems with variable sampling control. The goal is to design a sampled-data controller for global asymptotic stability, utilizing a novel approach with Lyapunov-Krasovskii functional and looped-functional and free-matrix-based inequality method. The proposed LMI conditions can be easily solved using MATLAB, and a numerical example is presented to demonstrate the benefits and superiority of the proposed scheme.