New Stabilization Conditions for Fuzzy-Based Sampled-Data Control Systems Using a Fuzzy Lyapunov Functional

Abstract

This paper focuses on the stabilization problem of Takagi-Sugeno fuzzy systems via a sampled-data controller using a fuzzy dependent functional. By employing a property of convex combination, a new approach to deal with the time derivatives of the fuzzy membership functions (FMFs) in the stabilization conditions is proposed, and less conservative conditions are derived in the form of linear matrix inequalities (LMIs). Moreover, the proposed approach introduces a switching function which opens up possibilities to use a switched controller and take advantage of its benefits well known in the literature. Therefore, two sampled-data control strategies are proposed, where the first one is a fuzzy controller and the second is a robust switched controller, that does not require the expressions of the FMFs to implement the control law, which guarantees the robustness of the controlled system in cases where the FMFs depend on uncertain parameters. Finally, the effectiveness of the proposed strategies is verified by two examples.