On topological entropy and stability of switched linear systems
On topological entropy and stability of switched linear systems
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DOI：
10.1145/3302504.3311815
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发表时间：
2019-04
期刊：
影响因子：
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通讯作者：
Guosong Yang;J. Hespanha;D. Liberzon
中科院分区：
文献类型：
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作者：
Guosong Yang;J. Hespanha;D. Liberzon
本文研究了切换线性系统的拓扑熵和稳定性特性。首先，我们证明切换线性系统解的指数增长率本质上是其拓扑熵的上限。其次，我们通过将切换线性系统分解为单位矩阵的标量倍数生成的部分和零熵的部分来估计切换线性系统的拓扑熵，并证明整体拓扑熵的上限是前者的拓扑熵。第三，我们证明，如果切换线性系统的拓扑熵在不稳定扰动下保持为零，则该系统是全局指数稳定的。最后，通过分解进行熵估计和基于熵的稳定性条件应用于三类切换线性系统，以构造新的拓扑熵上限和全局指数稳定性的新充分条件。
This paper studies topological entropy and stability properties of switched linear systems. First, we show that the exponential growth rates of solutions of a switched linear system are essentially upper bounded by its topological entropy. Second, we estimate the topological entropy of a switched linear system by decomposing it into a part that is generated by scalar multiples of the identity matrix and a part that has zero entropy, and proving that the overall topological entropy is upper bounded by that of the former. Third, we prove that a switched linear system is globally exponentially stable if its topological entropy remains zero under a destabilizing perturbation. Finally, the entropy estimation via decomposition and the entropy-based stability condition are applied to three classes of switched linear systems to construct novel upper bounds for topological entropy and novel sufficient conditions for global exponential stability.