Stability of a Class of Linear Switching Systems with Applications to Two Consensus Problems
Stability of a Class of Linear Switching Systems with Applications to Two Consensus Problems
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DOI：
10.1109/tac.2011.2176391
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发表时间：
2011-08
影响因子：
6.8
通讯作者：
Youfeng Su;Jie Huang
中科院分区：
文献类型：
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作者：
Youfeng Su;Jie Huang
本文首先建立了一类含有Kronecker积的线性切换系统的稳定性结果。这个问题很有趣，因为系统矩阵在任何时刻都不必是Hurwitz。这类线性切换系统出现在切换网络拓扑下的多智能体系统的控制中。作为这一稳定性结果的应用，我们给出了切换网络拓扑下一般边际稳定线性多智能体系统的无领导者一致性问题和领导者跟随一致性问题的可解性条件。与已有的结果不同，我们的结果仅假设动态图是一致连通的。
In this paper, we first establish a stability result for a class of linear switched systems involving Kronecker product. The problem is interesting in that the system matrix does not have to be Hurwitz at any time instant. This class of linear switched systems arises in the control of multi-agent systems under switching network topology. As applications of this stability result, we give the solvability conditions for both the leaderless consensus problem and the leader-following consensus problem for general marginally stable linear multi-agent systems under switching network topology. In contrast with some existing results, our results only assume that the dynamic graph is uniformly connected.