p. 231 - 241 Lyapunov operator inequalities for exponential stability of linear skew-product semiflows in Banach spaces Praţa C. 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 PDF Compressed Postscript Version to read ISSN 0862-9544 (Printed edition) Faculty of Mathematics, Physics and Informatics Comenius University 842 48 Bratislava, Slovak Republic Telephone: + 421-2-60295111 Fax: + 421-2-65425882 e-Mail: amuc@fmph.uniba.sk Internet: www.iam.fmph.uniba.sk/amuc © 2013, ACTA MATHEMATICA UNIVERSITATIS COMENIANAE |