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On the stability and control of nonlinear dynamical systems via vector lyapunov functions.

Bibliographic Details
Main Authors:	Nersesov, Sergey., Haddad, Wassim.
Format:	Villanova Faculty Authorship
Language:	English
Published:	2006
Online Access:	http://ezproxy.villanova.edu/login?url=https://digital.library.villanova.edu/Item/vudl:178322

Main Authors:

Nersesov, Sergey., Haddad, Wassim.

Format:

Villanova Faculty Authorship

Language:

English

Published:

2006

Online Access:

http://ezproxy.villanova.edu/login?url=https://digital.library.villanova.edu/Item/vudl:178322

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spelling	On the stability and control of nonlinear dynamical systems via vector lyapunov functions. Nersesov, Sergey. Haddad, Wassim. Vector Lyapunov theory has been developed to weaken the hypothesis of standard Lyapunov theory in order to enlarge the class of Lyapunov functions that can be used for analyzing system stability. In this paper, we extend the theory of vector Lyapunov functions by constructing a generalized comparison system whose vector field can be a function of the comparison system states as well as the nonlinear dynamical system states. Furthermore, we present a generalized convergence result which, in the case of a scalar comparison system, specializes to the classical Krasovskii-LaSalle invariant set theorem. In addition, we introduce the notion of a control vector Lyapunov function as a generalization of control Lyapunov functions, and show that asymptotic stabilizability of a nonlinear dynamical system is equivalent to the existence of a control vector Lyapunov function. Moreover, using control vector Lyapunov functions, we construct a universal decentralized feedback control law for a decentralized nonlinear dynamical system that possesses guaranteed gain and sector margins in each decentralized input channel. Furthermore, we establish connections between the recently developed notion of vector dissipativity and optimality of the proposed decentralized feedback control law. Finally, the proposed control framework is used to construct decentralized controllers for large-scale nonlinear systems with robustness guarantees against full modeling uncertainty. 2006 Villanova Faculty Authorship vudl:178322 IEEE TRANSACTIONS ON AUTOMATIC CONTROL 51 (2), February 2006, 203-215. en
dc.title_txt_mv	On the stability and control of nonlinear dynamical systems via vector lyapunov functions.
dc.creator_txt_mv	Nersesov, Sergey. Haddad, Wassim.
dc.description_txt_mv	Vector Lyapunov theory has been developed to weaken the hypothesis of standard Lyapunov theory in order to enlarge the class of Lyapunov functions that can be used for analyzing system stability. In this paper, we extend the theory of vector Lyapunov functions by constructing a generalized comparison system whose vector field can be a function of the comparison system states as well as the nonlinear dynamical system states. Furthermore, we present a generalized convergence result which, in the case of a scalar comparison system, specializes to the classical Krasovskii-LaSalle invariant set theorem. In addition, we introduce the notion of a control vector Lyapunov function as a generalization of control Lyapunov functions, and show that asymptotic stabilizability of a nonlinear dynamical system is equivalent to the existence of a control vector Lyapunov function. Moreover, using control vector Lyapunov functions, we construct a universal decentralized feedback control law for a decentralized nonlinear dynamical system that possesses guaranteed gain and sector margins in each decentralized input channel. Furthermore, we establish connections between the recently developed notion of vector dissipativity and optimality of the proposed decentralized feedback control law. Finally, the proposed control framework is used to construct decentralized controllers for large-scale nonlinear systems with robustness guarantees against full modeling uncertainty.
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author	Nersesov, Sergey. Haddad, Wassim.
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description	Vector Lyapunov theory has been developed to weaken the hypothesis of standard Lyapunov theory in order to enlarge the class of Lyapunov functions that can be used for analyzing system stability. In this paper, we extend the theory of vector Lyapunov functions by constructing a generalized comparison system whose vector field can be a function of the comparison system states as well as the nonlinear dynamical system states. Furthermore, we present a generalized convergence result which, in the case of a scalar comparison system, specializes to the classical Krasovskii-LaSalle invariant set theorem. In addition, we introduce the notion of a control vector Lyapunov function as a generalization of control Lyapunov functions, and show that asymptotic stabilizability of a nonlinear dynamical system is equivalent to the existence of a control vector Lyapunov function. Moreover, using control vector Lyapunov functions, we construct a universal decentralized feedback control law for a decentralized nonlinear dynamical system that possesses guaranteed gain and sector margins in each decentralized input channel. Furthermore, we establish connections between the recently developed notion of vector dissipativity and optimality of the proposed decentralized feedback control law. Finally, the proposed control framework is used to construct decentralized controllers for large-scale nonlinear systems with robustness guarantees against full modeling uncertainty.
title	On the stability and control of nonlinear dynamical systems via vector lyapunov functions.
title_full	On the stability and control of nonlinear dynamical systems via vector lyapunov functions.
title_fullStr	On the stability and control of nonlinear dynamical systems via vector lyapunov functions.
title_full_unstemmed	On the stability and control of nonlinear dynamical systems via vector lyapunov functions.
title_short	On the stability and control of nonlinear dynamical systems via vector lyapunov functions.
title_sort	on the stability and control of nonlinear dynamical systems via vector lyapunov functions.
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On the stability and control of nonlinear dynamical systems via vector lyapunov functions.
Nersesov, Sergey.
Haddad, Wassim.
Vector Lyapunov theory has been developed to weaken the hypothesis of standard Lyapunov theory in order to enlarge the class of Lyapunov functions that can be used for analyzing system stability. In this paper, we extend the theory of vector Lyapunov functions by constructing a generalized comparison system whose vector field can be a function of the comparison system states as well as the nonlinear dynamical system states. Furthermore, we present a generalized convergence result which, in the case of a scalar comparison system, specializes to the classical Krasovskii-LaSalle invariant set theorem. In addition, we introduce the notion of a control vector Lyapunov function as a generalization of control Lyapunov functions, and show that asymptotic stabilizability of a nonlinear dynamical system is equivalent to the existence of a control vector Lyapunov function. Moreover, using control vector Lyapunov functions, we construct a universal decentralized feedback control law for a decentralized nonlinear dynamical system that possesses guaranteed gain and sector margins in each decentralized input channel. Furthermore, we establish connections between the recently developed notion of vector dissipativity and optimality of the proposed decentralized feedback control law. Finally, the proposed control framework is used to construct decentralized controllers for large-scale nonlinear systems with robustness guarantees against full modeling uncertainty.
2006
Villanova Faculty Authorship
vudl:178322
IEEE TRANSACTIONS ON AUTOMATIC CONTROL 51 (2), February 2006, 203-215.
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On the stability and control of nonlinear dynamical systems via vector lyapunov functions.

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Nersesov, Sergey.
Haddad, Wassim.

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Vector Lyapunov theory has been developed to weaken the hypothesis of standard Lyapunov theory in order to enlarge the class of Lyapunov functions that can be used for analyzing system stability. In this paper, we extend the theory of vector Lyapunov functions by constructing a generalized comparison system whose vector field can be a function of the comparison system states as well as the nonlinear dynamical system states. Furthermore, we present a generalized convergence result which, in the case of a scalar comparison system, specializes to the classical Krasovskii-LaSalle invariant set theorem. In addition, we introduce the notion of a control vector Lyapunov function as a generalization of control Lyapunov functions, and show that asymptotic stabilizability of a nonlinear dynamical system is equivalent to the existence of a control vector Lyapunov function. Moreover, using control vector Lyapunov functions, we construct a universal decentralized feedback control law for a decentralized nonlinear dynamical system that possesses guaranteed gain and sector margins in each decentralized input channel. Furthermore, we establish connections between the recently developed notion of vector dissipativity and optimality of the proposed decentralized feedback control law. Finally, the proposed control framework is used to construct decentralized controllers for large-scale nonlinear systems with robustness guarantees against full modeling uncertainty.

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2006

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Nersesov, Sergey.
Haddad, Wassim.

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Haddad, Wassim.
On the stability and control of nonlinear dynamical systems via vector lyapunov functions.

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Haddad, Wassim.

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On the stability and control of nonlinear dynamical systems via vector lyapunov functions.

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On the stability and control of nonlinear dynamical systems via vector lyapunov functions.

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On the stability and control of nonlinear dynamical systems via vector lyapunov functions.

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On the stability and control of nonlinear dynamical systems via vector lyapunov functions.

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On the stability and control of nonlinear dynamical systems via vector lyapunov functions.

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On the stability and control of nonlinear dynamical systems via vector lyapunov functions.

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