Parametric quadratic stabilizability of uncertain nonlinear systems
type: Item
instance of: scholarly article
title: Parametric quadratic stabilizability of uncertain nonlinear systems
zbMATH Open document ID: 0808.93036
DOI: 10.1016/0167-6911(94)90087-6
published in: Systems \& Control Letters
publication date: 1995-03-09T00:00:00Z
review text: This paper deals with the problem of parametric quadratic stabilizability of nonlinear systems of the Lure-Postnikov type: \[ x'= [A+ \Delta A(p)]x+ [B+ \Delta B(p)] \mu(u), \] where \(p\) is the parameter vector and \(\mu(u)\) is a nonlinear function. When the system is linear, a number of powerful results related to \(Q\)-stabilizability are available. However, in these cases, it is assumed that the equilibrium of the uncertain system remains fixed in the origin despite the parametric and input disturbances. When a system is nonlinear as in the case considered in the paper, reference inputs and disturbances may alter the dynamics of the system in an essential way, by moving the equilibrium to a new location, or even destroying it. Thus, the results provided are a significant generalization of the previous theory. In particular, under assumptions on the nonlinearity, necessary and sufficient conditions for stabilizability of the system under linear static or dynamic state feedback are given.
Mathematics Subject Classification ID: 93C10
Mathematics Subject Classification ID: 93D09
Mathematics Subject Classification ID: 93C15
zbMATH DE Number: 612404
zbMATH Keywords: stabilizability
zbMATH Keywords: nonlinear systems
author: Yuzo Ohta
author: Dragoslav D. Siljak
reviewed by: Maria D. Di Benedetto
MaRDI profile type: Publication
full work available at URL: 0167-6911(94)90087-6
OpenAlex ID: W2087560842
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description: scientific article; zbMATH DE number 612404