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

Research output: Chapter in Book/Report/Conference proceedingChapterAcademicpeer-review

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.
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
StatePublished - 2002

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Hybrid systems
Dynamical systems
Trajectories

Cite this

Heemels, W. P. M. H., Camlibel, M. K., Schaft, van der, A. J., & Schumacher, J. M. (2002). On the existence and uniqueness of solution trajectories to hybrid dynamical systems. In R. Johannson, & A. Rantzer (Eds.), Nonlinear and hybrid systems in automotive control (pp. 391-421). London: Springer.
Heemels, W.P.M.H. ; Camlibel, M.K. ; Schaft, van der, A.J. ; Schumacher, J.M./ On the existence and uniqueness of solution trajectories to hybrid dynamical systems. Nonlinear and hybrid systems in automotive control. editor / R. Johannson ; A. Rantzer. London : Springer, 2002. pp. 391-421
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Heemels, WPMH, Camlibel, MK, Schaft, van der, AJ & Schumacher, JM 2002, On the existence and uniqueness of solution trajectories to hybrid dynamical systems. in R Johannson & A Rantzer (eds), Nonlinear and hybrid systems in automotive control. Springer, London, pp. 391-421.

On the existence and uniqueness of solution trajectories to hybrid dynamical systems. / Heemels, W.P.M.H.; Camlibel, M.K.; Schaft, van der, A.J.; Schumacher, J.M.

Nonlinear and hybrid systems in automotive control. ed. / R. Johannson; A. Rantzer. London : Springer, 2002. p. 391-421.

Research output: Chapter in Book/Report/Conference proceedingChapterAcademicpeer-review

TY - CHAP

T1 - On the existence and uniqueness of solution trajectories to hybrid dynamical systems

AU - Heemels,W.P.M.H.

AU - Camlibel,M.K.

AU - Schaft, van der,A.J.

AU - Schumacher,J.M.

PY - 2002

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N2 - 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.

AB - 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.

M3 - Chapter

SN - 1-85233-652-8

SP - 391

EP - 421

BT - Nonlinear and hybrid systems in automotive control

PB - Springer

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Heemels WPMH, Camlibel MK, Schaft, van der AJ, Schumacher JM. On the existence and uniqueness of solution trajectories to hybrid dynamical systems. In Johannson R, Rantzer A, editors, Nonlinear and hybrid systems in automotive control. London: Springer. 2002. p. 391-421.