Lyapunov operator inequalities for exponential stability
of linear skew-product semiflows in Banach spaces
Received: September 22, 2012; Accepted: March 14, 2013
Abstract. In the present paper we prove a sufficient condition and a characterization for the stability of linear skew-product semiflows by using Lyapunov function, in Banach spaces. These are generalizations of the results obtained in Ahmed N. U., Semigroups Theory with Applications to Systems and Control, Pittman Research, Notes Math., 1991. and Preda C. and Preda P., Lyapunov operator inequalities for exponential stability of Banach space semigroups of operators, Appl. Math. Letters 25(3) (2012), 401-403. for the case of C0-semigroups. Moreover, there are presented the discrete variants of the results mentioned above.
Keywords: linear skew-product semiflow; Lyapunov operator equation; exponential stability.
AMS Subject classification: Primary: 34D09, 37D25
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