Observer-Based $$H_\infty $$H∞ Sliding Mode Controller Design for Uncertain Stochastic Singular Time-Delay Systems

The paper is concerned with the observer-based $$H_\infty $$H∞ sliding mode controller design for a class of uncertain stochastic singular time-delay systems subjected to input nonlinearity. Using the sliding mode control, a robust law is established to guarantee the reachability of the sliding surface in a finite time interval, and the sufficient condition for asymptotic stability of the error system and sliding mode dynamics with disturbance attenuation level is presented in terms of linear matrix inequalities. Finally, an example illustrates the proposed method.