This article is concerned with the problem of guaranteed cost control for 2-D Markov jump Roesser systems with mismatched modes. The hidden Markov model is introduced to describe the asynchronous phenomenon caused by mismatched modes, and an asynchronous linear state-feedback control law is designed based on this model. With the help of the 2-D Lyapunov function and linear matrix inequality (LMI) techniques, sufficient conditions are established to ensure the asymptotic stability of the concerned system with a bound of the predefined guaranteed cost under three different boundary conditions, respectively. Finally, an algorithm that concludes the design processes of the optimal asynchronous guaranteed cost control law is proposed, and a numerical example is provided to verify its effectiveness.

中文翻译：

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二维马尔可夫Jump Roesser系统的异步保证成本控制


本文研究的是模态不匹配的二维马尔可夫跳Roesser系统的保证成本控制问题。引入隐马尔可夫模型来描述模式失配引起的异步现象，并基于该模型设计了异步线性状态反馈控制律。借助二维李亚普诺夫函数和线性矩阵不等式（LMI）技术，分别在三个不同的边界条件下建立了充分条件，以确保相关系统在预定义保证成本的范围内渐近稳定。最后，提出了一种算法，总结了最优异步保证成本控制律的设计过程，并通过数值算例验证了其有效性。