This paper states new sufficient conditions for the exponential stability of linear time-varying (LTV) systems of the form $dot x(cdot) = A(t) x(t)$. The approach proposed derives and uses the notion of perturbed frozen time (PFT) form that can be associated to any LTV system. Exploiting the Bellman-Gronwall lemma, relaxed stability conditions are then stated in terms of "average" parameter variations. Salient features of the approach are: pointwise stability of $A(cdot)$ is not required, $|dot A(cdot)|$ may not be bounded, the stability conditions also apply to uncertain systems. The approach is illustrated by numerical examples.

Relaxed conditions for the exponential stability of a class of linear time-varying systems / Ietto, Leopoldo; Orsini, Valentina. - In: IEEE TRANSACTIONS ON AUTOMATIC CONTROL. - ISSN 0018-9286. - 54:7(2009), pp. 1580-1585. [10.1109/TAC.2009.2015545]

Relaxed conditions for the exponential stability of a class of linear time-varying systems

IETTO, LEOPOLDO
;
ORSINI, Valentina
2009-01-01

Abstract

This paper states new sufficient conditions for the exponential stability of linear time-varying (LTV) systems of the form $dot x(cdot) = A(t) x(t)$. The approach proposed derives and uses the notion of perturbed frozen time (PFT) form that can be associated to any LTV system. Exploiting the Bellman-Gronwall lemma, relaxed stability conditions are then stated in terms of "average" parameter variations. Salient features of the approach are: pointwise stability of $A(cdot)$ is not required, $|dot A(cdot)|$ may not be bounded, the stability conditions also apply to uncertain systems. The approach is illustrated by numerical examples.
2009
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11566/36772
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