Feedback stabilization of nonlinear systems by locally bounded controls
type: Item
instance of: scholarly article
title: Feedback stabilization of nonlinear systems by locally bounded controls
zbMATH Open document ID: 0820.93053
DOI: 10.1016/0167-6911(94)90047-7
author: Minzhi Zhang
author: Ronald Hirschorn
published in: Systems \& Control Letters
publication date: 1995-09-14T00:00:00Z
review text: The paper considers the feedback stabilization and output regulation of a system affine in the control \(\dot x= f(x) + g(x)u\) (here \(u \in \mathbb{R}^ m\) is a vector), and output \(y = h(x)\). A Lyapunov functions approach is examined, where the existence of a Lyapunov function should imply the stabilization. This paper focuses on stabilization and regulation with locally bounded controls. Sufficient conditions are placed on the Lyapunov functions (or rather, on the interaction of this function with the control vector field), guaranteeing the boundedness, and further conditions guarantee the continuity at the origin. Enlightening comments and examples accompany the existence results.
Mathematics Subject Classification ID: 93D15
Mathematics Subject Classification ID: 93D30
zbMATH DE Number: 683617
zbMATH Keywords: bounded controls
zbMATH Keywords: feedback stabilization
zbMATH Keywords: Lyapunov functions
MaRDI profile type: Publication
full work available at URL: 0167-6911(94)90047-7
OpenAlex ID: W2081285646
cites work: Stabilization with relaxed controls
cites work: Q3309568
cites work: Passivity, feedback equivalence, and the global stabilization of minimum phase nonlinear systems
cites work: Q3140765
cites work: Asymptotic stabilization of two dimensional real analytic systems
cites work: Controllability and stability
cites work: Stability improvement of nonlinear systems by feedback
cites work: Stability theory for ordinary differential equations
cites work: Remarks on smooth feedback stabilization of nonlinear systems
cites work: A universal formula for stabilization with bounded controls
cites work: Adaptive output feedback tracking with almost disturbance decoupling for a class of nonlinear systems
cites work: Dynamic output feedback regulation for a class of nonlinear systems
cites work: A `universal' construction of Artstein's theorem on nonlinear stabilization
cites work: Q3975069
cites work: Sufficient Lyapunov-like conditions for stabilization
cites work: Output feedback stabilization
cites work: Q5651936
reviewed by: Zvi Artstein
description: scientific article; zbMATH DE number 683617