Exponential stability of linear periodic difference-delay equations
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866911309739589632 |
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| author | Baratchart, Laurent Fueyo, Sébastien Pomet, Jean-Baptiste |
| author_facet | Baratchart, Laurent Fueyo, Sébastien Pomet, Jean-Baptiste |
| contents | This paper deals with the stability of linear periodic difference delay systems, where the value at time $t$ of a solution is a linear combination with periodic coefficients of its values at finitely many delayed instants $t-τ_1,\ldots,t-τ_N$. We establish a necessary and sufficient condition for exponential stability of such systems when the coefficients have Hölder-continuous derivative, that generalizes the one obtained for difference delay systems with constant coefficients by Henry and Hale in the 1970s. This condition may be construed as analyticity, in a half plane, of the (operator valued) harmonic transfer function of an associated linear control system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2201_12066 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Exponential stability of linear periodic difference-delay equations Baratchart, Laurent Fueyo, Sébastien Pomet, Jean-Baptiste Optimization and Control Dynamical Systems Functional Analysis This paper deals with the stability of linear periodic difference delay systems, where the value at time $t$ of a solution is a linear combination with periodic coefficients of its values at finitely many delayed instants $t-τ_1,\ldots,t-τ_N$. We establish a necessary and sufficient condition for exponential stability of such systems when the coefficients have Hölder-continuous derivative, that generalizes the one obtained for difference delay systems with constant coefficients by Henry and Hale in the 1970s. This condition may be construed as analyticity, in a half plane, of the (operator valued) harmonic transfer function of an associated linear control system. |
| title | Exponential stability of linear periodic difference-delay equations |
| topic | Optimization and Control Dynamical Systems Functional Analysis |
| url | https://arxiv.org/abs/2201.12066 |