A generalized fractional Halanay inequality and its applications
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929538617835520 |
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| author | Thinh, L. V. Tuan, H. T. |
| author_facet | Thinh, L. V. Tuan, H. T. |
| contents | This paper is concerned with a generalized Halanay inequality and its applications to fractional-order delay linear systems. First, based on a sub-semigroup property of Mittag-Leffler functions, a generalized Halanay inequality is established. Then, applying this result to fractional-order delay systems with an order-preserving structure, an optimal estimate for the solutions is given. Next, inspired by the obtained Halanay inequality, a linear matrix inequality is designed to derive the Mittag-Leffler stability of general fractional-order delay linear systems. Finally, numerical examples are provided to illustrate the proposed theoretical results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_09370 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A generalized fractional Halanay inequality and its applications Thinh, L. V. Tuan, H. T. Dynamical Systems 34A08, 34K37, 45A05, 45M05, 45M20, 33E12, 26D10, 15A39 This paper is concerned with a generalized Halanay inequality and its applications to fractional-order delay linear systems. First, based on a sub-semigroup property of Mittag-Leffler functions, a generalized Halanay inequality is established. Then, applying this result to fractional-order delay systems with an order-preserving structure, an optimal estimate for the solutions is given. Next, inspired by the obtained Halanay inequality, a linear matrix inequality is designed to derive the Mittag-Leffler stability of general fractional-order delay linear systems. Finally, numerical examples are provided to illustrate the proposed theoretical results. |
| title | A generalized fractional Halanay inequality and its applications |
| topic | Dynamical Systems 34A08, 34K37, 45A05, 45M05, 45M20, 33E12, 26D10, 15A39 |
| url | https://arxiv.org/abs/2410.09370 |