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Communication Dans Un Congrès Année : 2023

On Input-to-State Stability of Linear Difference Equations and Its Characterization with a Lyapunov Functional

Jean Auriol
Delphine Bresch-Pietri

Résumé

This paper investigates necessary and sufficient Lyapunov conditions for Input-to-State Stability (ISS) of Linear Difference Equations with pointwise delays and an additive exogenous signal. Grounding on recent works in the literature on necessary conditions for the exponential stability of such Difference Equations, we propose a quadratic Lyapunov functional involving the derivative of the so-called delay Lyapunov matrix of the corresponding homogeneous Difference Equation. We prove that the ISS of Linear Difference Equations is equivalent to the existence of an ISS Lyapunov functional. We apply this result to the stability and ISS analysis of hyperbolic Partial Differential Equations of conservation laws.
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Dates et versions

hal-04051122 , version 1 (30-03-2023)

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Jean Auriol, Delphine Bresch-Pietri. On Input-to-State Stability of Linear Difference Equations and Its Characterization with a Lyapunov Functional. 22nd World Congress of the International Federation of Automatic Control (IFAC 2023), Jul 2023, Yokohama, Japan. ⟨10.1016/j.ifacol.2023.10.1684⟩. ⟨hal-04051122⟩
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