The event-based H∞H_{\infty} control problem is investigated for a class of nonhomogeneous Markov jump systems (MJSs) with partially unknown transition probabilities (TPs). The MJS is characterized by a piecewise nonhomogeneous Markovian chain, where the switching of the system TP matrix is governed by a higher-level chain. A hidden Markov model (HMM) is employed to observe the system mode, which cannot always be correctly detected in practice. Under this framework, the partially unknown TPs existing in both higher-level TPs (HTPs) and conditional TPs (CTPs) are taken into account for practical consideration. Additionally, an observed-mode-dependent event-triggered mechanism (ETM) is employed to design an asynchronous controller, which is expected to alleviate the burden of the communication network. Evidently, the considered scenario is fairly general and covers some special cases. With the above consideration, sufficient conditions are established to guarantee stochastic stability of the resulting closed-loop system with a prescribed H∞H_{\infty} performance. Finally, two examples are presented to demonstrate the effectiveness and applicability of the proposed method.

中文翻译：

---

具有不完美转移概率的非齐次马尔可夫跳跃系统的基于事件的异步 $H_{\infty}$ 控制


针对一类具有部分未知转移概率 (TP) 的非齐次马尔可夫跳跃系统 (MJS)，研究基于事件的 H∞H_{\infty} 控制问题。 MJS 的特点是分段非齐次马尔可夫链，其中系统 TP 矩阵的切换由更高级别的链控制。采用隐马尔可夫模型（HMM）来观察系统模式，但在实践中并不总是能正确检测到。在此框架下，出于实际考虑，较高级别TP（HTP）和条件TP（CTP）中存在的部分未知TP都被考虑在内。此外，采用观察模式相关的事件触发机制（ETM）来设计异步控制器，有望减轻通信网络的负担。显然，所考虑的场景相当普遍，并且涵盖了一些特殊情况。通过上述考虑，建立了充分的条件来保证所得到的闭环系统具有规定的 H∞H_{\infty} 性能的随机稳定性。最后，通过两个例子证明了该方法的有效性和适用性。