The method of several Lyapunov functions in the global stabilization problem for nonlinear systems
type: Item
instance of: scholarly article
zbMATH Open document ID: 0989.93084
author: V. A. Brusin
author: B. L. Mazov
publication date: 2002-08-05T00:00:00Z
Mathematics Subject Classification ID: 93D30
Mathematics Subject Classification ID: 93D15
Mathematics Subject Classification ID: 34D20
zbMATH DE Number: 1577658
zbMATH Keywords: stabilization
zbMATH Keywords: composite systems
zbMATH Keywords: discontinuous feedback
zbMATH Keywords: Lyapunov functions
zbMATH Keywords: inverted pendulum
MaRDI profile type: Publication
title: The method of several Lyapunov functions in the global stabilization problem for nonlinear systems
published in: Differential Equations
review text: The authors consider composite systems of the form NEWLINE\[NEWLINE\begin{cases} \dot x=f(x,y,v,u) \\ \dot y=g(x,y,v,u) \\ v^{(q)}=h(v,\dot v,\dots,v^{(q-1)}) \end{cases} \tag{1}NEWLINE\]NEWLINE with discontinuous feedback \(u=U(x,y)\). Assuming that \(V\) and \(W\) are known Lyapunov functions for the subsystems defined by the first two equations respectively, they prove that for all solutions of (1), \((x(t), y(t))\) converges to zero when \(t\to +\infty\). The result is applied to the problem of stabilizing an inverted pendulum on a controlled trolley subject to an unknown force.
reviewed by: Andrea Bacciotti
description: scientific article