Stabilization of a hybrid system with a nonlinear nonmonotone feedback

Free access article

Issue		ESAIM: COCV Volume 4, 1999


Page(s)		123 - 135
DOI		10.1051/cocv:1999106

DOI: 10.1051/cocv:1999106

ESAIM: COCV, April 1999, Vol. 4, p. 123-135

Stabilization of a hybrid system with a nonlinear nonmonotone feedback

Stabilisation d'un système hybride avec feedback non linéaire et non monotone.

Eduard FEIREISL
Institut of Mathematics AVCR, Zitna 25, 11567 Prague 1, République Tchèque; (feireisl@math.cas.cz)

Geoffrey O'DOWD
Institut Élie Cartan, BP. 239, 54506 Vand $\oe$ uvre-lès-Nancy, France; (odowd@iecn.u-nancy.fr)

Received March 27, 1998. Revised November 30, 1998.

Abstract: For a hybrid system composed of a cable with masses at both ends, we prove the existence of solutions for a class of nonlinear and nonmonotone feedback laws by means of a priori estimates. Assuming some local monotonicity, strong stabilization is obtained thanks to some Riemann's invariants technique and La Salle's principle.

Résumé: Pour un système hybride constitué d'un câble aux extrémités duquel sont accrochées deux masses, on prouve l'existence de solutions pour une classe de lois de feedbacks non linéaires et non monotones grâce à des estimations a priori. Une hypothèse de monotonie locale combinée à une technique d'invariants de Riemann permet de se ramener à un semi-groupe contractant pour lequel le principe de La Salle conduit à la stabilité forte du système.

Keywords and phrases: Hybrid systems, wave equation, stabilization by feedback law, Riemann invariants

AMS Subject Classification: 93D15, 47H20

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