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Stability and stabilizability for linear systems of difference equations. (English) Zbl 1064.39011

Authors’ abstract: The aim of this paper is to characterize the uniform exponential stability of difference equations. We obtain very general input-output conditions for stability of difference equations using diverse vector valued sequence spaces. As an application, we obtain an estimation for the lower bound of the stability radius of a linear control system of difference equations. Finally, we characterize the stability of systems of difference equations in terms of stabilizability and detectability, obtaining discrete-time versions for a result due to St. Clark, Yu. Latushkin, St. Montgomery-Smith and T. Randolph [SIAM J. Control Optimization 38, No. 6, 1757–1793 (2000; Zbl 0978.47030)].

MSC:

39A11 Stability of difference equations (MSC2000)
93C55 Discrete-time control/observation systems
93D15 Stabilization of systems by feedback

Citations:

Zbl 0978.47030
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References:

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