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Lyapunov Functionals that Lead to Exponential Stability and Instability in Finite Delay Volterra Difference Equations
Catherine Kublik, Youssef Raffoul

 

Abstract

We use Lyapunov functionals to obtain sufficient conditions that guarantee exponential stability of the zero solution of the finite delay Volterra difference equation x ( t + 1 ) = a ( t ) x ( t ) + s = t r t 1 b ( t , s ) x ( s ) . Also, by displaying a slightly different Lyapunov functional, we obtain conditions that guarantee the instability of the zero solution. The highlight of the paper is the relaxing of the condition |a(t)| < 1. Moreover, we provide examples in which we show that our theorems provide an improvement of some recent results.

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