Triangular systems: A global extension of the Coron-Praly theorem on the existence of feedback-integrator stabilisers
type: Item
instance of: scholarly article
title: Triangular systems: A global extension of the Coron-Praly theorem on the existence of feedback-integrator stabilisers
zbMATH Open document ID: 0882.93071
DOI: 10.1016/S0947-3580(97)70060-8
published in: European Journal of Control
publication date: 1998-03-02T00:00:00Z
review text: This paper deals with single-input, nonlinear smooth systems in the so-called triangular form \[ \begin{cases} \dot x_1= f_1(x_1,x_2)\\ \dot x_2= f_2(x_1,x_2,x_3)\\ \cdots\cdots\cdots\cdots\cdots\cdots\cdots\\ \dot x_n= f_n(x_1,x_2,\dots, x_n,v)\end{cases}\tag{1} \] The problem is to find a function \(u(x_1,\dots, x_{n+1})\) such that the origin of \(\mathbb{R}^{n+1}\) becomes a globally asymptotically stable equilibrium for (1), with \(v= x_{n+1}\) and the additional equation \(\dot x_{n+1}= u\). The author establishes sufficient conditions for the solution to this problem. The feedback law \(u\) turns out to be continuous, and of class \(C^1\) on \(\mathbb{R}^{n+1}\backslash\{0\}\). The conditions are satisfied, for instance, in the case where the \(f_i\)'s are polynomials.
Mathematics Subject Classification ID: 93D15
Mathematics Subject Classification ID: 93C10
zbMATH DE Number: 1057556
zbMATH Keywords: stabilization
zbMATH Keywords: dynamic feedback
zbMATH Keywords: triangular form
author: J. Tsinias
reviewed by: Andrea Bacciotti
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1057556