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On the stability of impulsively perturbed differential systems

Published online by Cambridge University Press:  17 April 2009

S.G. Pandit
S.G. Pandit
Affiliation:
Department of Mathematics, Centre for Post-graduate Instruction and Research, University of Bombay, Panaji, Goa, India.
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Abstract

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This paper deals with the study of uniform asymptotic stability of the measure differential system Dx = F(t, x) + G(t, x)Du, where the symbol D stands for the derivative in the sense of distributions. The system is viewed as a perturbed system of the ordinary differential system x' = F(t, x), where the perturbation term G(t, x)Du is impulsive and the state of the system changes suddenly at the points of discontinuity of u. It is shown, under certain conditions, that the uniform asymptotic stability property of the unperturbed system is shared by the perturbed system. To do this, the well-known Gronwall integral inequality is generalized so as to be applicable to Lebesgue-Stieltjes integrals.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 17 , Issue 3 , December 1977 , pp. 423 - 432
Copyright
Copyright © Australian Mathematical Society 1977

References

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