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Zbl 1093.93023
de la Sen, M.
Asymptotic hyperstability under unstructured and structured modeling deviations from the linear behavior. (English)
[J] Nonlinear Anal., Real World Appl. 7, No. 2, 248-264 (2006). ISSN 1468-1218

Summary: This paper deals with the asymptotic hyperstability of nominally asymptotic hyperstable linear systems in the presence of unstructured modeling errors. It is assumed that the nominal plant is linear, time-invariant and of strictly positive real transfer function with the feedback loop satisfying a Popov's type input-output time integral inequality for all time and the combination resulting in an asymptotically hyperstable closed-loop system. The current plant is assumed to be subjected, in general, unstructured deviations from its nominal behavior but then asymptotic hyperstability results are also obtained for particular structured modeling errors like time-varying linear dynamics, bilinear or delay-dependent dynamics. The key technique used for obtaining the results is to guarantee that a measure of the input/output energy of the forward current dynamics is positive and uniformly bounded for all time for certain amounts of modeling errors provided that the nominal one exhibits the same property.

MSC 2000:: *93D10 Popov-type stability of feedback systems
34D20 Lyapunov stability of ODE

Keywords: Asymptotic Lyapunov stability; hyperstability; asymptotic hyperstability; Positive/strict positive realness

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