Adaptive stabilization of non-necessarily inversely stable first-order systems by using estimates modification based on testing the Sylvester determinant
type: Item
instance of: scholarly article
title: Adaptive stabilization of non-necessarily inversely stable first-order systems by using estimates modification based on testing the Sylvester determinant
zbMATH Open document ID: 1029.93055
DOI: 10.1016/S0096-3003(02)00252-7
published in: Applied Mathematics and Computation
publication date: 2003-09-15T00:00:00Z
review text: This paper presents an algorithms for adaptive stabilization of first-order continuous time systems with a zero that can be stable or unstable. Parameter modification of only one parameter is used by the adaptive scheme. Neither hysteresis switching nor reliance on the properties of the covariance matrix are required. Instead, singularities are avoided through a modification of the a priori estimated plant parameters so that the associated Sylvester matrix is guaranteed to be nonsingular. Nonsingularity is achieved by insuring that the absolute value of the determinant of the Sylvester matrix exceeds a positive threshold. The author first provides the adaptive stabilization results for the nominal plant and proves the global asymptotic stability of the closed-loop system. The results are then extended to the case where plant uncertainties are present in the form of bounded noise and a standard class of unmodelled dynamics. Global stability of the scheme is again established. Some brief comments about extensions of this approach to second-order systems are also provided.
Mathematics Subject Classification ID: 93D21
zbMATH DE Number: 1981451
zbMATH Keywords: chattering motion
zbMATH Keywords: Sylvester determinant
zbMATH Keywords: unmodelled dynamics
zbMATH Keywords: parameter modification
zbMATH Keywords: adaptive stabilization
zbMATH Keywords: singularities
zbMATH Keywords: Sylvester matrix
author: M. De la Sen
reviewed by: William J. Satzer Jr.
MaRDI profile type: Publication
Wikidata QID: Q57675677
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full work available at URL: s0096-3003(02)00252-7
OpenAlex ID: W2121060498
DBLP publication ID: journals/amc/Sen03
description: scientific article; zbMATH DE number 1981451