Uniform Exponential Stability of Discrete Evolution Families on Space of p-Periodic Sequences
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...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/784289 |
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| Summary: | 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. |
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| ISSN: | 1085-3375 1687-0409 |