This article studies a class of asynchronous generalized H₂ control problems for continuous‐time discrete‐state semi‐Markov jump linear systems. By constructing a Lyapunov function based on the semi‐Markov process, introducing a weak infinitesimal operator and applying the smoothness of the expectation, sufficient conditions are obtained to ensure stochastic stability and generalized H₂ performance of the system. Simultaneously, equivalent conditions are given by introducing slack variables and an asynchronous controller is designed. Moreover, we derive the sufficient conditions for the case where the transition rate is partially unknown. Finally, we use the cone complement linearization iterative algorithm to simulate two examples to prove the effectiveness of the design scheme.

中文翻译：

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具有半马尔可夫跳变的线性系统的广义H2控制

本文研究了连续时间离散状态半马氏跳线性系统的一类异步广义H ₂控制问题。通过基于半马尔可夫过程构造一个Lyapunov函数，引入一个弱无穷小算子并应用期望的平滑性，可以获得足够的条件来确保随机稳定性和广义H ₂系统的性能。同时，通过引入松弛变量给出等效条件，并设计了一个异步控制器。此外，我们导出了过渡速率部分未知的情况的充分条件。最后，我们使用锥补码线性化迭代算法对两个实例进行仿真，以证明设计方案的有效性。