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Mathematical Problems in Engineering
Volume 3 (1997), Issue 3, Pages 203-215

Robust stability of nonlinear piecewise deterministic systems under matching conditions

Mechanical Engineering Department, École Polytechnique de Montréal, P.O. Box 6079, Station, “Centre-ville”, Montréal, Que., Canada

Received 6 March 1996

Copyright © 1997 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper deals with the robustness of the class of nonlinear piecewise deterministic systems with unknown but bounded uncertainties. Under the assumption that all the modes of the markovian jump process (disturbance) communicate, the complete access to the system state and the boundedness of the uncertainties, a sufficient condition for stochastic stability of this class of systems is given. An example is presented to validate the proposed results.