Stability criteria of nonlinear generalized proportional fractional delayed systems
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929533975789568 |
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| author | Zitane, Hanaa Torres, Delfim F. M. |
| author_facet | Zitane, Hanaa Torres, Delfim F. M. |
| contents | This work deals with the finite time stability of generalized proportional fractional systems with time delay. First, based on the generalized proportional Grönwall inequality, we derive an explicit criterion that enables the system trajectories to stay within a priori given sets during a pre-specified time interval, in terms of the Mittag-Leffler function. Then, we investigate the finite time stability of nonlinear nonhomogeneous delayed systems by means of an approach based on Hölder's and Jensen's inequalities. Numerical applications are presented to illustrate the validity and feasibility of the developed results. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_12256 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stability criteria of nonlinear generalized proportional fractional delayed systems Zitane, Hanaa Torres, Delfim F. M. Optimization and Control Dynamical Systems 26A33, 34A08, 34A34, 34D20, 34K20 This work deals with the finite time stability of generalized proportional fractional systems with time delay. First, based on the generalized proportional Grönwall inequality, we derive an explicit criterion that enables the system trajectories to stay within a priori given sets during a pre-specified time interval, in terms of the Mittag-Leffler function. Then, we investigate the finite time stability of nonlinear nonhomogeneous delayed systems by means of an approach based on Hölder's and Jensen's inequalities. Numerical applications are presented to illustrate the validity and feasibility of the developed results. |
| title | Stability criteria of nonlinear generalized proportional fractional delayed systems |
| topic | Optimization and Control Dynamical Systems 26A33, 34A08, 34A34, 34D20, 34K20 |
| url | https://arxiv.org/abs/2405.12256 |