Nonsynchronous Model Reduction for Uncertain 2-D Markov Jump Systems
研究了模式信息不完全可获取时，二维马尔可夫跳变系统的非同步H∞模型降阶问题，基于隐马尔可夫模型处理非同步现象，并提出了设计方法。
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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal H_{\infty }$ </tex-math></inline-formula> 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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal H_{\infty }$ </tex-math></inline-formula> 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.