Robust ${maths\cr H}_{\infty }$ Control of T–S Fuzzy Time-Delay Systems via a New Sliding-Mode Control Scheme

This paper addresses the sliding-mode control (SMC) design problem for a class of uncertain nonlinear systems that can be represented by Takagi-Sugeno (T-S) fuzzy models. We propose a novel dynamic sliding-mode control scheme for T-S fuzzy models, aiming to eliminate the restrictive assumption that all subsystems share a common input matrix, which is required in most existing fuzzy SMC approaches. Sufficient conditions for the reachability of the sliding surface and asymptotic stability of the sliding motion are formulated in the form of linear matrix inequalities. Finally, simulation results that illustrate the advantages and effectiveness of the proposed approaches are provided.