In this work, the result of reachable set bounding and extended dissipative control synthesis of the Markovian jump time-delayed system is studied subject to stochastic actuator failures and partially known transition probabilities. Specifically, a novel actuator fault model is designed, in which the actuator fault matrix satisfies a certain probabilistic condition. Under the construction of an appropriate Lyapunov–Krasovskii functional (LKF), as well as reciprocal convex approach, Jensen’s integral inequality, and reachable set lemma, delay-dependent sufficient criteria are obtained in terms of linear matrix inequalities (LMIs) for finding an ellipsoid to bound the reachable sets of the Markovian jump time-delayed system with bounded disturbances. Finally, two numerical examples are provided to validate the effectiveness of the proposed strategy.

中文翻译：

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具有有界扰动的马尔可夫跳跃时滞系统的扩展耗散控制

在这项工作中，研究了随机执行器故障和部分已知的转移概率的情况下，马尔可夫跳跃时滞系统的可达集界和扩展耗散控制综合的结果。具体地，设计了一种新型的执行器故障模型，其中执行器故障矩阵满足一定的概率条件。在构造适当的Lyapunov–Krasovskii泛函（LKF）以及倒数凸方法，Jensen积分不等式和可到达集引理的基础上，获得了依赖于延迟的足够标准，用于寻找椭球体用有界扰动来限制马尔可夫跳跃时滞系统的可达集。最后，提供了两个数值示例来验证所提出策略的有效性。