Automatica ( IF 6.4 ) Pub Date : 2022-12-30 , DOI: 10.1016/j.automatica.2022.110812 Yuqian Guo, Fang Lu, Weihua Gui
This paper studies the mean-square stability of discrete-time linear switched systems with random switching, where the switching signal is the output of a logic dynamical switching model driven by an independent and identically distributed (i.i.d.) process. This class of switching is referred to as the modeled random switching. By regarding the switching model as a part of the system, a combined switched system with i.i.d. switching is obtained, which is of a hybrid nature, that is, the augmented state vector has both logic and continuous components. The semi-tensor product of matrices and the vector representation of logic are applied to merge the logic and the continuous components of the state. The equivalence between the mean-square stability of the original switched system and that of the merged switched system under i.i.d. switching is proved. By deriving the dynamics of the column-stacking form of the covariance matrix, necessary and sufficient conditions of mean-square stability for discrete-time linear switched systems with modeled random switching are obtained. An illustrative example is provided to demonstrate the usage of the proposed results.
中文翻译:
建模随机切换下离散时间切换系统的均方稳定性
本文研究了具有随机切换的离散时间线性切换系统的均方稳定性,其中切换信号是由独立同分布 (iid) 过程驱动的逻辑动态切换模型的输出。此类切换称为建模随机切换。将切换模型视为系统的一部分,得到了具有iid切换的组合切换系统,具有混合性质,即增广状态向量既有逻辑分量又有连续分量。应用矩阵的半张量积和逻辑的向量表示来合并逻辑和状态的连续分量。iid下原切换系统与合并切换系统均方稳定性的等价性 切换被证明。通过推导协方差矩阵的列堆叠形式的动力学,获得了具有建模随机切换的离散时间线性切换系统均方稳定性的充分必要条件。提供了一个说明性示例来演示建议结果的使用。