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On exponential dichotomy in Banach spaces
Published online by Cambridge University Press: 17 April 2009
Abstract
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In this paper we study the exponential dichotomy property for linear systems, the evolution of which can be described by a semigroup of class C0 on a Banach space. We define the class of (p, q) dichotomic semigroups and establish the connections between the dichotomy concepts and admissibility property of the pair (Lp, Lq) for linear control systems. The obtained results are generalizations of well-known results of W.A. Coppel, J.L. Massera and J.J. Schäffer, K.J. Palmer.
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- Copyright © Australian Mathematical Society 1981
References
[1]Balakrishnan, A.V., Applied functional analysis (Applications of Mathematics, 3. Springer-Verlag, New York, Heidelberg, Berlin, 1976).Google Scholar
[2]Coppel, W.A., Dichotomies in stability theory (Lecture Notes in Mathematics, 629. Springer-Verlag, Berlin, Heidelberg, New York, 1978).CrossRefGoogle Scholar
[3]Hillie, Einar, Phillips, Ralph S., Functional analysis and semi-groups, revised edition (American Mathematical Society Colloquium Publications, 31. American Mathematical Society, Providence, Rhode Island, 1957).Google Scholar
[4]Massera, José Luis, Schäffer, Juan Jorge, Linear differential equations and function spaces (Pure and Applied Mathematics, 21. Academic Press, New York and London, 1966).Google Scholar
[5]Megan, M., “On exponential stability of linear control systems in Hilbert spaces”, An. Univ. Timisoaro Ser. Sti. Mat. 14 (1976), 125–130.Google Scholar
[6]Megan, Mihail, “On the input-output stability of linear controllable systems”, Canad. Math. Bull. 21 (1978), 187–195.CrossRefGoogle Scholar
[7]Palmer, K.J., “Two linear systems criteria for exponential dichotomy”, Ann. Mat. Pura Appl. (to appear).Google Scholar
[8]Perron, Oskar, “Die Stabilitätsfrage bei Differentialgleichungen”, Math. Z. 32 (1930), 703–728.CrossRefGoogle Scholar
[9]Silverman, L.M. and Anderson, B.D.O., “Controllability, observability and stability of linear systems”, SIAM J. Control Optim. 6 (1968), 121–130.CrossRefGoogle Scholar
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