Connection between almost everywhere stability of an ODE and advection PDE

Rajeev Rajaram; Umesh Vaidya; Makan Fardad

doi:10.1109/CDC.2007.4434827

Connection between almost everywhere stability of an ODE and advection PDE

Rajeev Rajaram, Umesh Vaidya, Makan Fardad

Research output: Chapter in Book/Entry/Poem › Conference contribution

9 Scopus citations

Abstract

A result on the necessary and sufficient conditions for almost everywhere stability of an invariant set in continuoustime dynamical systems is presented. It is shown that the existence of a Lyapunov density is equivalent to the almost everywhere stability of an invariant set. Furthermore, such a density can be obtained as the positive solution of a linear partial differential equation analogous to the positive solution of Lyapunov equation for stable linear systems.

Original language	English (US)
Title of host publication	Proceedings of the 46th IEEE Conference on Decision and Control 2007, CDC
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	5880-5885
Number of pages	6
ISBN (Print)	1424414989, 9781424414987
DOIs	https://doi.org/10.1109/CDC.2007.4434827
State	Published - 2007
Externally published	Yes
Event	46th IEEE Conference on Decision and Control 2007, CDC - New Orleans, LA, United States Duration: Dec 12 2007 → Dec 14 2007

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Other

Other	46th IEEE Conference on Decision and Control 2007, CDC
Country/Territory	United States
City	New Orleans, LA
Period	12/12/07 → 12/14/07

ASJC Scopus subject areas

Control and Systems Engineering
Modeling and Simulation
Control and Optimization

Access to Document

10.1109/CDC.2007.4434827

Cite this

Rajaram, R., Vaidya, U., & Fardad, M. (2007). Connection between almost everywhere stability of an ODE and advection PDE. In Proceedings of the 46th IEEE Conference on Decision and Control 2007, CDC (pp. 5880-5885). Article 4434827 (Proceedings of the IEEE Conference on Decision and Control). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2007.4434827

Connection between almost everywhere stability of an ODE and advection PDE. / Rajaram, Rajeev; Vaidya, Umesh; Fardad, Makan.
Proceedings of the 46th IEEE Conference on Decision and Control 2007, CDC. Institute of Electrical and Electronics Engineers Inc., 2007. p. 5880-5885 4434827 (Proceedings of the IEEE Conference on Decision and Control).

Research output: Chapter in Book/Entry/Poem › Conference contribution

Rajaram, R, Vaidya, U & Fardad, M 2007, Connection between almost everywhere stability of an ODE and advection PDE. in Proceedings of the 46th IEEE Conference on Decision and Control 2007, CDC., 4434827, Proceedings of the IEEE Conference on Decision and Control, Institute of Electrical and Electronics Engineers Inc., pp. 5880-5885, 46th IEEE Conference on Decision and Control 2007, CDC, New Orleans, LA, United States, 12/12/07. https://doi.org/10.1109/CDC.2007.4434827

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AB - A result on the necessary and sufficient conditions for almost everywhere stability of an invariant set in continuoustime dynamical systems is presented. It is shown that the existence of a Lyapunov density is equivalent to the almost everywhere stability of an invariant set. Furthermore, such a density can be obtained as the positive solution of a linear partial differential equation analogous to the positive solution of Lyapunov equation for stable linear systems.

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ER -

Connection between almost everywhere stability of an ODE and advection PDE

Abstract

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ASJC Scopus subject areas

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