Stabilization of nonlinear systems by similarity transformations
type: Item
instance of: scholarly article
title: Stabilization of nonlinear systems by similarity transformations
zbMATH Open document ID: 0922.34053
DOI: 10.1155/S1048953398000422
published in: Journal of Applied Mathematics and Stochastic Analysis
publication date: 1999-10-14T00:00:00Z
full work available at URL: https://eudml.org/doc/48249
review text: The author considers the system: \[ \dot x=A(x)+ b(x)u \] where the pair \(A(x)\), \(b(x)\) is given and \(x\in\mathbb{R}^n\), \(u(x)= s^*(x)x\). She obtains the feedback vector \(s(x)\) to stabilize the corresponding closed loop system. For an arbitrarily chosen constant vector \(g\), a sufficient condition on the existence and an explicite form of a similarity transformation \(T(A(x), b(x),g)\) is established. This latter transforms the matrix \(A(x)\) into a Frobenius matrix, vector \(b(x)\) into \(g\), and an unknown feedback vector \(s(x)\) into the first unit vector. The stabilization of the transformed system is subject to the choice of the constant vector \(g\).
Mathematics Subject Classification ID: 34H05
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 1247739
zbMATH Keywords: feedback vector
zbMATH Keywords: closed loop system
zbMATH Keywords: Frobenius matrix
author: Irina Efremovna Zuber
reviewed by: Stefan Balint
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1247739