This paper investigates input–output finite-time reliable static output feedback (SOF) control of a time-varying system under the influence of both input time delay and actuator failures. An actuator fault model consisting of linear and nonlinear faults is considered during the time-varying control process. The objective is to design a reliable SOF controller that can ensure input–output finite-time stability (IO-FTS) of the resulting closed-loop system. An augmented time-varying Lyapunov functional is constructed, in which some Lyapunov matrices are variable function of time ${t}$ . By dividing the time interval and delay interval into equal segments, the matrix-valued functions are expressed by a linear interpolation formula. Moreover, combining with the single and double Wirtinger-based integral inequalities, delay-dependent IO-FTS conditions are derived. It is shown that the SOF control issue is solved in forms of linear matrix inequalities. In the end, the effectiveness is demonstrated by simulations.

中文翻译：

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输入延迟时变系统的输入输出有限时间可靠静态输出控制

本文研究了在输入时间延迟和执行器故障的影响下时变系统的输入-输出有限时间可靠静态输出反馈 (SOF) 控制。在时变控制过程中考虑了由线性和非线性故障组成的执行器故障模型。目标是设计一个可靠的 SOF 控制器，以确保最终闭环系统的输入-输出有限时间稳定性 (IO-FTS)。构造了一个增广的时变 Lyapunov 泛函，其中一些 Lyapunov 矩阵是时间 ${t}$ 的变函数。通过将时间间隔和延迟间隔分成相等的部分，矩阵值函数用线性插值公式表示。此外，结合基于单双 Wirtinger 的积分不等式，导出依赖于延迟的 IO-FTS 条件。结果表明，SOF 控制问题以线性矩阵不等式的形式解决。最后，通过仿真证明了有效性。