Deng Yushu, Wang Shihao, Zheng Shiqi, Li Haiming, Jian Haitao, Tang Xiaoqi
Shaoyang Institute of Advanced Manufacturing Technology, Shaoyang 422000, China.
School of Automation, China University of Geosciences, Wuhan 430074, China.
Entropy (Basel). 2022 Aug 15;24(8):1126. doi: 10.3390/e24081126.
This paper addresses the asynchronous stabilization problem of two typical stochastic switching systems, i.e., dual switching systems and semi-Markov jump systems. By dual switching, it means that the systems contain both deterministic and stochastic switching dynamics. New stability criteria are firstly proposed for these two switched systems, which can well handle the asynchronous phenomenon. The conditional expectation of Lyapunov functions is allowed to increase during some unmatched interval to reduce the conservatism. Next, we present numerically testable asynchronous controller design methods for the dual switching systems. The proposed method is suitable for the situation where the asynchronous modes come from both inaccurate mode detection and time varying delay. Meanwhile, the transition probabilities are both uncertain and partly accessible. Finally, novel asynchronous controller design methods are proposed for the semi-Markov jump systems. The sojourn time of the semi-Markov jump systems can have both lower and upper bounds, which could be more practical than previous scenarios. Examples are utilized to demonstrate the effectiveness of the proposed methods.
本文研究了两种典型随机切换系统，即双切换系统和半马尔可夫跳跃系统的异步镇定问题。通过双切换，意味着系统同时包含确定性和随机切换动态。首先针对这两种切换系统提出了新的稳定性准则，该准则能够很好地处理异步现象。允许李雅普诺夫函数的条件期望在某些不匹配区间内增加，以降低保守性。接下来，我们提出了双切换系统的数值可验证异步控制器设计方法。所提出的方法适用于异步模式来自不准确模式检测和时变延迟的情况。同时，转移概率既不确定且部分可获取。最后，针对半马尔可夫跳跃系统提出了新颖的异步控制器设计方法。半马尔可夫跳跃系统的逗留时间可以有上下界，这可能比以前的情况更具实际意义。通过实例验证了所提方法的有效性。
