Robust Stability for Uncertain Fuzzy Systems with Time-delay Based on Sampled-Data Control

Abstract

In this paper, we address the robust stability for un-certain fuzzy systems with time-varying delays based on sampled-data control. By developing some new terms, an improved piecewise Lyapunov-Krasovskii functional (LKF) is constructed to take full advantage of characteristic about real sampling pattern. Furthermore, some relaxed matrices proposed in the LKF are not necessarily positive definite. By using the LKF and Free-Matrix-Based (FMB) integral inequality, some sufficient criteria are established to ensure the stability of fuzzy systems and reduce the influence of external disturbance with an $\mathcal{H}_{\infty}$ norm bound. Then, the memory sampled-data controller can be derived by solving a group of linear matrix inequalities (LMIs) with the maximal sampling period. Finally, a numerical example is given to demonstrate the benefits and the superiority of the approach proposed.