马尔可夫跳跃线性系统的符号稳定研究

Research on Symbolic Stability of Markov Jump Linear Systems

分析马尔可夫跳跃线性系统在没有数值条件下的稳定性,仅考虑子系统矩阵和马尔可夫转移概率矩阵的元素符号。结果表明,分析一种名为符号稳定的定性稳定,将符号稳定的概念引入马尔可夫跳跃线性系统的均方稳定中,得到马尔可夫跳跃线性系统的均方符号。相比于基于Lyapunov稳定性理论的鲁棒控制方法,该文所分析的符号稳定可避免求解线性矩阵不等式,更符合工程设计的系统。

In this paper, the stability of Markov jump linear systems without numerical conditions is analyzed. Only the element symbols of subsystem matrix and Markov transition probability matrix are considered. The result is that a kind of qualitative stability called symbolic stability is analyzed, the concept of symbolic stability is introduced into the mean square stability of Markov jump linear systems, and the mean square symbols of Markov jump linear systems are obtained.Compared with the robust control method based on Lyapunov stability theory, the symbolic stability analyzed in this paper avoids solving linear matrix inequalities and is more suitable for engineering design.