In this paper, the $H_{\infty }$ optimal control problem for a Markovian jump linear system (MJLS) over multiple lossy communication channels is considered. It is assumed that the controller communicates with each actuator through a different communication channel. We solve the $H_{\infty }$ optimization problem for the system with a Transmission Control Protocol (TCP) using the theory of dynamic games and obtain a state feedback controller. The infinite horizon $H_{\infty }$ optimization problem is analysed as a limiting case of the finite horizon optimization problem. Then, we obtain the corresponding state feedback controller and show that it stabilizes the closed-loop system in the face of random packet dropouts. A novel and relaxed condition for stability of the closed-loop system with the saddle-point policy is also presented. Further, we show that a weaker notion of observability is sufficient to establish our results.

中文翻译：

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H∞ 多有损通信信道上跳跃系统的最优控制

在本文中，考虑了马尔可夫跳跃线性系统（MJLS）在多个有损通信信道上的$H_{\infty}$最优控制问题。假设控制器通过不同的通信通道与每个致动器通信。我们利用动态博弈理论解决了具有传输控制协议（TCP）系统的$H_{\infty}$优化问题，并获得了状态反馈控制器。无限视野$H_{\infty }$优化问题被分析为有限视野优化问题的极限情况。然后，我们获得了相应的状态反馈控制器，并表明它在面对随机数据包丢失时稳定了闭环系统。还提出了具有鞍点策略的闭环系统稳定性的一种新颖而宽松的条件。进一步，