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This paper considers the problem of the robust stability for the nonlinear system with time-varying delay and parameters uncertainties. Based on the H∞ theorem, Lyapunov-Krasovskii theory, and linear matrix inequality (LMI) optimization technique, the H∞ quasi-sliding mode controller and switching function are developed such that the nonlinear system is asymptotically stable in the quasi-sliding mode and satisfies the disturbance attenuation (H∞-norm performance). The effectiveness and accuracy of the proposed methods are shown in numerical simulations.

Robust Stability for Nonlinear Systems with Time-Varying Delay and Uncertainties via the H∞ Quasi-Sliding Mode Control