H∞ sliding mode control for discrete-time singular systems with time-varying delay

In this paper, the problem of H
_∞
sliding mode control for discrete-time singular systems with time-varying delay is studied. A new type of sliding mode surface involving the singular matrix E is proposed firstly, based on which, a less conservative condition is obtained to guarantee the ideal sliding mode dynamics of the singular system to be admissible with a γ-Ievel disturbance attenuation of the unmatched disturbance. Then by constructing an estimation of the time-varying delay term, a Iinear SMC Iaw is proposed to guarantee that the system states converge into a vicinity of the ideal sliding surface. Finally, numerical examples are provided to demonstrate the effectiveness of the presented method.