Mode information is of great significance when investigating the Markov jump systems (MJSs). However, it is common in practical scenarios that the mode information is not completely accessible, which probably induces nonsynchronization problems. Taking this into consideration, in this article, we study nonsynchronous H∞\mathcal H_{\infty } model order reduction for 2-D MJSs with model uncertainty. The considered 2-D system and reduced-order model are characterized by the Roesser model. The nonsynchronization phenomenon between the original system and the reduced-order model is dealt with under the framework of the hidden Markov model. By appropriately selecting the Lyapunov function, the asymptotic mean-square stability and the H∞\mathcal H_{\infty } performance of the error system are analyzed, and sufficient conditions are proposed. Based on this, an efficient design method for nonsynchronous model order reduction is further proposed with the help of a projection lemma. Finally, the correctness and effectiveness of the designed reduced-order model are verified through some simulations.

中文翻译：

---

不确定二维马尔可夫跳跃系统的非同步模型简化


在研究马尔可夫跳跃系统（MJS）时，模态信息具有重要意义。然而，在实际场景中，模式信息不完全可访问的情况很常见，这可能会引发不同步问题。考虑到这一点，在本文中，我们研究了具有模型不确定性的二维 MJS 的非同步 H∞\mathcal H_{\infty } 模型降阶。所考虑的二维系统和降阶模型由 Roesser 模型来表征。在隐马尔可夫模型的框架下处理了原系统与降阶模型之间的不同步现象。通过适当选择Lyapunov函数，分析了误差系统的渐近均方稳定性和H∞\mathcal H_{\infty }性能，并提出了充分条件。在此基础上，借助投影引理，进一步提出了一种高效的异步模型降阶设计方法。最后，通过仿真验证了所设计的降阶模型的正确性和有效性。