Delay-dependent robust stability of uncertain discrete singular time-delay systems with nonlinear disturbance

The problem of robust stability analysis for uncertain discrete singular time-delay systems with nonlinear disturbance is investigated. The nominal system is not assumed to be necessarily regular and causal. By decomposing the nominal system into slow and fast subsystems, a linear matrix inequality (LMI) condition is proposed for a discrete singular time-delay system to be regular, causal and stable. Based on this, an LMI criterion is obtained for robust stability of an uncertain discrete singular time-delay system. Two examples are provided to demonstrate the feasibility of the proposed approach.