Stabilization with relaxed controls

Artstein, Zvi

doi:10.1016/0362-546x(83)90049-4

Cited by 884 publications

(558 citation statements)

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“…Definition 2.1 (see [1,7]). A smooth, proper, and positive definite function V is a control Lyapunov function (LCF) for system (2.1) if for…”

Section: Preliminariesmentioning

confidence: 99%

“…Since the concept of Lyapunov control function was first introduced by Arstein [1], many results have been obtained for the stabilization of nonlinear control systems using the Lyapunov control function approach, e.g., [2,[5][6][7][9][10][11][12]. Among them, Moulay and Perruquetti gave a formula for the continuous stabilizers for system (1.1) in the single-input case via a known Lyapunov control function [7].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Constructive Stabilization of Quadratic-Input Nonlinear Systems with Bounded Controls

Zhong

Cheng

2008

J Dyn Control Syst

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Abstract. In this paper, the stabilization of quadratic-input nonlinear systems with bounded controls is considered. According to the type of quadratic-input forms, two cases, namely, positive definite and positive semi-definite, are considered. For the case of positive definiteness, a universal formula for bounded stabilizers is given via a known Lyapunov control function. For the case of positive semidefiniteness, a constructive parametrization of bounded stabilizers is proposed under the assumption that there exists a known Lyapunov control function with respect to a smaller control set than the admissible control set.

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“…Definition 2.1 (see [1,7]). A smooth, proper, and positive definite function V is a control Lyapunov function (LCF) for system (2.1) if for…”

Section: Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Constructive Stabilization of Quadratic-Input Nonlinear Systems with Bounded Controls

Zhong

Cheng

2008

J Dyn Control Syst

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“…Detailed description about CLF, can be found in [22] and [37] - [39]. Let us illustrate the idea of CLF with a simple example [40].…”

Section: Chapter 3 Theoretical Backgroundmentioning

confidence: 99%

Multichoice Control Strategy for VSC-HVdc

Latorre¹,

Ghandhari²,

Söder³

2007

2007 iREP Symposium - Bulk Power System Dynamics and Control - VII. Revitalizing Operational Reliability

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“…In the recent works [22] and [23], the concept of Weak Global Asymptotic Stabilization by Sampled-Data Feedback (SDF-WGAS) is introduced for autonomous systems: This condition constitutes an extension of the well-known "Artstein-Sontag" sufficient condition for asymptotic stabilization of systems (1.2) by means of an almost smooth feedback; (see [3], [19] and [21]). Throughout the paper we adopt the following notations.…”

Section: Introductionmentioning

confidence: 99%