On the existence and uniqueness of solution trajectories to hybrid dynamical systems

W.P.M.H. Heemels, M.K. Camlibel, A.J. Schaft, van der, J.M. Schumacher

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Abstract

In this paper, we study the fundamental system-theoretic property of wellposedness for several classes of hybrid dynamical systems. Hybrid systems are characterized by the presence and interaction of continu-ous dynamics and discrete actions. Many different description formats have been proposed in recent years for such systems; some proposed forms are quite direct, others lead to rather indirect descriptions. The more indirect a description form is, the harder it becomes to show that solutions are well-defined. This paper intends to provide a survey on the available results on existence and uniqueness of solutions for given initial conditions in the context of various description formats for hybrid systems.
Original languageEnglish
Title of host publicationNonlinear and hybrid systems in automotive control
EditorsR. Johannson, A. Rantzer
Place of PublicationLondon
PublisherSpringer
Pages391-421
Number of pages31
ISBN (Print)1-85233-652-8
Publication statusPublished - 2002

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