Uniform Exponential Stability of Discrete Evolution Families on Space of p-Periodic Sequences. (31st August 2014)

• Record Type: Journal Article
• Authors: Wang, Yongfang; Zada, Akbar; Ahmad, Nisar; Lassoued, Dhaou; Li, Tongxing
• Other Names: Wang Qi-Ru Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2014(2014)
• Publication Date: 2014-08-31
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2014/784289
• Languages: English
• ISSNs: 1085-3375

Abstract

Abstract : We prove that the discrete system ζ n + 1 = A n ζ n is uniformly exponentially stable if and only if the unique solution of the Cauchy problem ζ n + 1 = A n ζ n + e i θ n + 1 z n + 1, n ∈ Z +, ζ 0 = 0, is bounded for any real number θ and any p -periodic sequence z ( n ) with z ( 0 ) = 0 . Here, A n is a sequence of bounded linear operators on Banach space X .