Global state and feedback equivalence of nonlinear systems
type: Item
instance of: scholarly article
title: Global state and feedback equivalence of nonlinear systems
zbMATH Open document ID: 0577.93029
DOI: 10.1016/0167-6911(85)90072-6
published in: Systems \& Control Letters
publication date: 1985-01-01T00:00:00Z
review text: The problem of finding global state space transformations and global feedback of the form \(u(t)=\alpha (x)+v(t)\) to transform a given nonlinear system \(\dot x=f(x)+g(x)u\) to a controllable linear system on \(R^ n\) or on an open subset of \(R^ n\) is considered here. A complete set of differential geometric conditions which are equivalent to the existence of a solution to the above problem are presented. The solution presented here is valid in the \(C^ k\) situation where \(2n+1\leq k\leq \omega\) and agrees with \textit{W. Respondek}'s solution [''Global aspects of linearization, equivalence to polynomial forms and decomposition of nonlinear control systems'', Algebraic and geometric methods in nonlinear control, Proc. CNRS Conf., Paris 1985] in the analytic case which was obtained independently. In a subsequent paper [''Global linearization by feedback and state transformations'', Decision and control, Proc. IEEE Conf. Dec. 1985] the authors extended the results to the multiinput case and to the case of more general feedback (i.e. \(u(t)=\alpha (x)+\beta (x)v(t))\).
Mathematics Subject Classification ID: 93C10
Mathematics Subject Classification ID: 57R27
Mathematics Subject Classification ID: 93B17
Mathematics Subject Classification ID: 93C15
zbMATH DE Number: 3924619
zbMATH Keywords: linearization
zbMATH Keywords: global state space transformations
zbMATH Keywords: global feedback
zbMATH Keywords: nonlinear system
author: W. P. Dayawansa
author: William M. Boothby
author: David Elliott
MaRDI profile type: Publication
full work available at URL: 0167-6911(85)90072-6
OpenAlex ID: W2076809784
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description: scientific article; zbMATH DE number 3924619