H∞ Control for Stochastic Singular Systems With Time-Varying Delays via Sampled-Data Controller
针对随机奇异时变时滞系统，设计了一种采样数据控制器，通过构建新型时变不连续Lyapunov-Krasovskii泛函，推导出保证系统随机容许性的条件，并给出了控制器设计方法。
In this article, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${H}_{\infty }$ </tex-math></inline-formula> 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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${H}_{\infty }$ </tex-math></inline-formula> 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.