Necessary conditions for exponential stability of linear neutral type systems with multiple time delays |
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Authors: | Ning Zhao Xian Zhang Yu Xue Peng Shi |
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Affiliation: | 1. School of Mathematical Science, Heilongjiang University, Harbin 150080, China;2. College of Automation, Harbin Engineering University, Harbin, 150001, China;3. College of Engineering and Science, Victoria University, Melbourne, VIC 8001, Australia |
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Abstract: | In this paper, we will give necessary conditions for the exponential stability of linear neutral type systems with multiple time delays by employing the Lyapunov–Krasovskii functional approach. These conditions not only extend the existing results of the neutral-delay-free systems, but also provide a new tool for stability analysis of linear neutral type systems with multiple time delays by characterizing instability domains. As a medium step, we will investigate several crucial properties which are involved with both the fundamental matrix and Lyapunov matrix. Numerical examples illustrate the validity of the theoretical results. |
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Keywords: | Corresponding author. |
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