This paper addresses the problem of delay-dependent robust and reliable $\mathscr {H}_{\infty }$ static output feedback (SOF) control for a class of uncertain discrete-time Takagi–Sugeno fuzzy-affine (FA) systems with time-varying delay and actuator faults in a singular system framework. The Markov chain is employed to describe the actuator faults behaviors. In particular, by utilizing a system augmentation approach, the conventional closed-loop system is converted into a singular FA system. By constructing a piecewise-Markovian Lyapunov–Krasovskii functional, a new $\mathscr {H}_{\infty }$ performance analysis criterion is then presented, where a novel summation inequality and S-procedure are succeedingly employed. Subsequently, thanks to the special structure of the singular system formulation, the piecewise-affine SOF controller design is proposed via a convex program. Lastly, illustrative examples are given to show the efficacy and less conservatism of the presented approach.

中文翻译：

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具有时滞和执行器故障的仿射系统的可靠输出反馈控制的分段马尔可夫Lyapunov方法

本文解决了依赖于延迟的鲁棒性和可靠性问题 $ \ mathscr {H} _ {\ infty} $ 一类不确定系统具有时变时滞和执行器故障的一类不确定离散Takagi-Sugeno模糊仿射（FA）系统的静态输出反馈（SOF）控制。马尔可夫链用于描述执行器故障行为。特别地，通过利用系统扩充方法，常规的闭环系统被转换成单一的FA系统。通过构造分段马尔可夫Lyapunov–Krasovskii泛函，一个新的 $ \ mathscr {H} _ {\ infty} $ 然后提出了性能分析标准，并成功地采用了一个新的求和不等式和S-过程。随后，由于奇异系统公式的特殊结构，通过凸程序提出了分段仿射SOF控制器设计。最后，通过举例说明该方法的有效性和保守性。