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This paper is devoted to the robust ℋ ∞ sliding mode control issue for a type of switched discrete singular systems with time-varying delays under arbitrary switching. Since the system states are not available, the nonfragile observer strategy is used to generate the state estimation. By designing a novel sliding surface function, which is established on the estimation, new sufficient conditions via linear matrix inequalities are derived so that the closed-loop system is admissible with an ℋ ∞ disturbance attenuation level . Furthermore, sliding mode controllers are given to guarantee the reachability of the quasi-sliding mode and weaken the chattering. At last, examples are presented to verify the validity of our provided approach.

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