Exponential stability of gradient systems with applications to nonlinear-in-control design methods

Eugene Lavretsky; Chengyu Cao; Naira Hovakimyan

doi:10.1109/ACC.2007.4282429

Exponential stability of gradient systems with applications to nonlinear-in-control design methods

Eugene Lavretsky, Chengyu Cao, Naira Hovakimyan

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

Exponential stability analysis for gradient systems is the primary focus of this paper. Sufficient conditions are derived that guarantee exponential stability for both autonomous and parameter-dependent gradient systems. These conditions require boundedness of singular values of a Jacobian matrix, uniformly in the system state space. The reported theoretical results are subsequently applied to design tracking controllers for a class of nonlinear-in-control dynamical systems. The design is carried out using time-scale separation techniques.

Original language	English (US)
Title of host publication	Proceedings of the 2007 American Control Conference, ACC
Pages	6003-6008
Number of pages	6
DOIs	https://doi.org/10.1109/ACC.2007.4282429
State	Published - 2007
Externally published	Yes
Event	2007 American Control Conference, ACC - New York, NY, United States Duration: Jul 9 2007 → Jul 13 2007

Publication series

Name	Proceedings of the American Control Conference
ISSN (Print)	0743-1619

Other

Other	2007 American Control Conference, ACC
Country/Territory	United States
City	New York, NY
Period	7/9/07 → 7/13/07

ASJC Scopus subject areas

Electrical and Electronic Engineering

Online availability

10.1109/ACC.2007.4282429

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Exponential stability of gradient systems with applications to nonlinear-in-control design methods. / Lavretsky, Eugene; Cao, Chengyu; Hovakimyan, Naira.
Proceedings of the 2007 American Control Conference, ACC. 2007. p. 6003-6008 4282429 (Proceedings of the American Control Conference).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Lavretsky, E, Cao, C & Hovakimyan, N 2007, Exponential stability of gradient systems with applications to nonlinear-in-control design methods. in Proceedings of the 2007 American Control Conference, ACC., 4282429, Proceedings of the American Control Conference, pp. 6003-6008, 2007 American Control Conference, ACC, New York, NY, United States, 7/9/07. https://doi.org/10.1109/ACC.2007.4282429

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N2 - Exponential stability analysis for gradient systems is the primary focus of this paper. Sufficient conditions are derived that guarantee exponential stability for both autonomous and parameter-dependent gradient systems. These conditions require boundedness of singular values of a Jacobian matrix, uniformly in the system state space. The reported theoretical results are subsequently applied to design tracking controllers for a class of nonlinear-in-control dynamical systems. The design is carried out using time-scale separation techniques.

AB - Exponential stability analysis for gradient systems is the primary focus of this paper. Sufficient conditions are derived that guarantee exponential stability for both autonomous and parameter-dependent gradient systems. These conditions require boundedness of singular values of a Jacobian matrix, uniformly in the system state space. The reported theoretical results are subsequently applied to design tracking controllers for a class of nonlinear-in-control dynamical systems. The design is carried out using time-scale separation techniques.

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Exponential stability of gradient systems with applications to nonlinear-in-control design methods

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