Improved stability criteria for linear time-varying systems on time scales |
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Authors: | Xiaodong Lu Zhi Liu |
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Affiliation: | 1. School of Control Science and Engineering, Shandong University, Jinan, People's Republic of China https://orcid.org/0000-0003-4473-7410;2. School of Control Science and Engineering, Shandong University, Jinan, People's Republic of China |
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Abstract: | ABSTRACT In this paper, asymptotic stability problems of linear time-varying (LTV) systems on time scales are considered based on a less conservative Lyapunov inequality, whose right side is not required to be necessarily negative. It is shown that the Lyapunov inequality covers not only the corresponding trivial (continuous and discrete) ones but also nontrivial ones. Based on this inequality, some necessary and sufficient conditions for asymptotic stability, exponential stability, uniformly exponential stability of LTV systems on time scales are obtained. An example about nontrivial systems is given for illustrating the effectiveness of the proposed results. |
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Keywords: | Linear time-varying systems asymptotic stability Lyapunov inequality time scale |
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