${{H}}_{∞}$ Control for Stochastic Singular Systems With Time-Varying Delays via Sampled-Data Controller

In this article, ${{H}}_{infinity}$ control for stochastic singular time-varying delay systems under arbitrarily variable samplings is addressed via designing a sampled-data controller. The first and foremost, a novel time-dependent discontinuous Lyapunov-Krasovskii (L-K) functional is built, which takes good advantage of the factual sampling pattern's available properties. Then, based on the refined input delay method by utilizing the constructed time-dependent L-K functional, the free-weighting matrix method, and the auxiliary vector function approach are adopted to develop conditions ensuring the stochastic admissibility for the studied stochastic singular systems with time-varying delays. On the basis of the derived conditions, the sampled-data ${{H}}_{infinity}$ control issue is tackled, and an unambiguous expression for the sampled-data controller design method is obtained. Finally, simulation examples manifest that our proposed results are correct and effective.