Lyapunov Type Theorems for Exponential Stability of Linear Skew-Product Three-Parameter Semiflows with Discrete Time
For linear skew-product three-parameter semiflows with discrete time acting on an arbitrary Hilbert space, we obtain a complete characterization of exponential stability in terms of the existence of appropriate Lyapunov functions. As a nontrivial application of our work, we prove that the notion of...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-04-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/9/2/47 |
| _version_ | 1797569503762055168 |
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| author | Davor Dragičević Ciprian Preda |
| author_facet | Davor Dragičević Ciprian Preda |
| author_sort | Davor Dragičević |
| collection | DOAJ |
| description | For linear skew-product three-parameter semiflows with discrete time acting on an arbitrary Hilbert space, we obtain a complete characterization of exponential stability in terms of the existence of appropriate Lyapunov functions. As a nontrivial application of our work, we prove that the notion of an exponential stability persists under sufficiently small linear perturbations. |
| first_indexed | 2024-03-10T20:12:32Z |
| format | Article |
| id | doaj.art-814e5eda3ac44ca68b8da15ac2c2b062 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-10T20:12:32Z |
| publishDate | 2020-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-814e5eda3ac44ca68b8da15ac2c2b0622023-11-19T22:51:18ZengMDPI AGAxioms2075-16802020-04-01924710.3390/axioms9020047Lyapunov Type Theorems for Exponential Stability of Linear Skew-Product Three-Parameter Semiflows with Discrete TimeDavor Dragičević0Ciprian Preda1Department of Mathematics, University of Rijeka, Radmile Matejčić 2, 51000 Rijeka, CroatiaDepartment of Mathematics, Faculty of Mathematics and Computer Science, West University of Timişoara, V. Pârvan Blvd. No. 4, 300223 Timişoara, RomaniaFor linear skew-product three-parameter semiflows with discrete time acting on an arbitrary Hilbert space, we obtain a complete characterization of exponential stability in terms of the existence of appropriate Lyapunov functions. As a nontrivial application of our work, we prove that the notion of an exponential stability persists under sufficiently small linear perturbations.https://www.mdpi.com/2075-1680/9/2/47exponential stabilitylinear skew-product semiflowsLyapunov functions |
| spellingShingle | Davor Dragičević Ciprian Preda Lyapunov Type Theorems for Exponential Stability of Linear Skew-Product Three-Parameter Semiflows with Discrete Time Axioms exponential stability linear skew-product semiflows Lyapunov functions |
| title | Lyapunov Type Theorems for Exponential Stability of Linear Skew-Product Three-Parameter Semiflows with Discrete Time |
| title_full | Lyapunov Type Theorems for Exponential Stability of Linear Skew-Product Three-Parameter Semiflows with Discrete Time |
| title_fullStr | Lyapunov Type Theorems for Exponential Stability of Linear Skew-Product Three-Parameter Semiflows with Discrete Time |
| title_full_unstemmed | Lyapunov Type Theorems for Exponential Stability of Linear Skew-Product Three-Parameter Semiflows with Discrete Time |
| title_short | Lyapunov Type Theorems for Exponential Stability of Linear Skew-Product Three-Parameter Semiflows with Discrete Time |
| title_sort | lyapunov type theorems for exponential stability of linear skew product three parameter semiflows with discrete time |
| topic | exponential stability linear skew-product semiflows Lyapunov functions |
| url | https://www.mdpi.com/2075-1680/9/2/47 |
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