Contraction Analysis of Time-Delay Systems
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866916068299112448 |
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| author | Watanabe, Rintaro Kawano, Yu |
| author_facet | Watanabe, Rintaro Kawano, Yu |
| contents | In this paper, we investigate contraction analysis for nonlinear time-delay systems described by functional differential equations. We first extend the concept of Lyapunov-Krasovskii functionals within the differential framework. We then show that its existence is equivalent to that of an incremental Lyapunov-Krasovskii functional and guarantees uniform incremental exponential stability. Next, we extend the concept of Lyapunov-Razumikhin functions within the differential framework, whose existence also ensures uniform incremental exponential stability. As an application of our results, we formulate stabilizing feedback control design for nonlinear time-delay systems with single delays in terms of linear matrix inequalities. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2606_00179 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Contraction Analysis of Time-Delay Systems Watanabe, Rintaro Kawano, Yu Systems and Control Optimization and Control In this paper, we investigate contraction analysis for nonlinear time-delay systems described by functional differential equations. We first extend the concept of Lyapunov-Krasovskii functionals within the differential framework. We then show that its existence is equivalent to that of an incremental Lyapunov-Krasovskii functional and guarantees uniform incremental exponential stability. Next, we extend the concept of Lyapunov-Razumikhin functions within the differential framework, whose existence also ensures uniform incremental exponential stability. As an application of our results, we formulate stabilizing feedback control design for nonlinear time-delay systems with single delays in terms of linear matrix inequalities. |
| title | Contraction Analysis of Time-Delay Systems |
| topic | Systems and Control Optimization and Control |
| url | https://arxiv.org/abs/2606.00179 |