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

Yongfang Wang, Akbar Zada, Nisar Ahmad, Dhaou Lassoued and Tongxing Li

Abstract and Applied Analysis, 2014, vol. 2014, issue 1

Abstract: 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.

Date: 2014
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https://doi.org/10.1155/2014/784289

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:784289

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