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A new version of a theorem of Minh-Räbiger-Schnaubelt regarding nonautonomous evolution equations. (English) Zbl 1228.93110

Summary: We develop a new version of a known theorem obtained by Nguyen Van Minh, F. Räbiger and R. Schnaubelt [Integral Equations Oper. Theory 32, No. 3, 332–353 (1998; Zbl 0977.34056)]. We rely completely on the classical ‘test functions’ method designed by Perron in 1930. The advantage of such a version is that is more readable since the classical method of Perron have been known for decades and that we do not involve a sophisticated mathematical machinery. Our approach is in contrast with the general philosophy of ‘autonomization’ the nonautonomous system, since we do not require to attach the evolution semigroup. Also we point out a discrete-time version of our approach extending some known results given by Li and Henry.

MSC:

93D25 Input-output approaches in control theory
93D20 Asymptotic stability in control theory
34G10 Linear differential equations in abstract spaces
37D20 Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.)
34C45 Invariant manifolds for ordinary differential equations

Citations:

Zbl 0977.34056
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References:

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