Abstract
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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