Unified stability criteria for slowly time-varying and switched linear systems
Unified stability criteria for slowly time-varying and switched linear systems
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DOI：
10.1016/j.automatica.2018.06.025
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发表时间：
2018-10
期刊：
影响因子：
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通讯作者：
Xiaobin Gao;D. Liberzon;Ji Liu;T. Başar
中科院分区：
文献类型：
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作者：
Xiaobin Gao;D. Liberzon;Ji Liu;T. Başar
本文提出了一种统一的方法来制定稳定性条件的慢时变线性系统和切换线性系统。将全变差的概念推广到矩阵值函数的情形。利用这一推广的概念，得到了一个结果，推广了已有的慢时变线性系统的稳定性条件。作为这一结果的特例，得到了线性切换系统的两组稳定性条件，它们与文献中的已知结果一致。最后通过一个数值例子进一步说明了主要结果的应用。
This paper presents a unified approach to formulating stability conditions for slowly time-varying linear systems and switched linear systems. The concept of total variation is generalized to the case of matrix-valued functions. Using this generalized concept, a result extending existing stability conditions for slowly time-varying linear systems is derived. As special cases of this result, two sets of stability conditions are derived for switched linear systems, which match known results in the literature. A numerical example is included to further illustrate the application of the main result.