Uniform Exponential Stability of Discrete Evolution Families on Space of p-Periodic Sequences

Abstract EN

We prove that the discrete system ζn+1=Anζn is uniformly exponentially stable if and only if the unique solution of the Cauchy problem ζn+1=Anζn+eiθn+1zn+1, n∈Z+, ζ0=0, is bounded for any real number θ and any p-periodic sequence z(n) with z(0)=0.

Here, An is a sequence of bounded linear operators on Banach space X.