Adaptive $$H_{\infty }$$H∞ Integral Sliding Mode Control for Uncertain Singular Time-Delay Systems Based on Observer

This paper is concerned with the robust $$H_{\infty }$$H∞ control for a class of uncertain singular time-delay systems via a novel sliding mode observer scheme. Firstly, a particularly non-fragile observer is introduced to estimate the unmeasured states, and a novel integral sliding surface function is presented. Then, a sufficient condition for the admissibility and specified $$H_{\infty }$$H∞ performance of the resultant sliding mode dynamics of the closed-loop systems is derived in terms of linear matrix inequality. At last, the finite-time reachability of the predesigned sliding surface is guaranteed by utilizing the adaptive sliding mode control law from the initial time. An illustrative example is provided to verify the potential and superiority of the method with comparisons.