Representing a nonlinear state space system as a set of higher-order differential equations in the inputs and outputs
type: Item
instance of: scholarly article
title: Representing a nonlinear state space system as a set of higher-order differential equations in the inputs and outputs
zbMATH Open document ID: 0669.93011
DOI: 10.1016/0167-6911(89)90008-X
published in: Systems \& Control Letters
publication date: 1989-01-01T00:00:00Z
full work available at URL: http://www.sciencedirect.com/science/journal/01676911
review text: The paper is concerned with the problem of transforming a smooth nonlinear control system with outputs in the state space representation into an equivalent input-output (external) representation. The problem recently has attracted considerable attention within the differential algebraic approach in control theory. In this paper a strict algorithm is presented which realizes the transformation locally, provided that certain rank conditions are satisfied. As the result the dynamics of the initial system are restricted to an unobservable part of state variables, while the remaining state variables are expressed in terms of jets of input and output functions, and the external behaviour of the system is found. The approach assumed in the paper resembles in the spirit that of \textit{Chun-Wen Li} and \textit{Yuan-Kun Feng} [Int. J. Control 45, 1147-1160 (1987; Zbl 0622.93028)].
Mathematics Subject Classification ID: 93B17
Mathematics Subject Classification ID: 93B20
Mathematics Subject Classification ID: 93C10
Mathematics Subject Classification ID: 93B07
zbMATH DE Number: 4097197
zbMATH Keywords: equivalence
zbMATH Keywords: state space representation
zbMATH Keywords: external behaviour
zbMATH Keywords: smooth nonlinear control system
zbMATH Keywords: differential algebraic approach
author: Arjan van der Schaft
reviewed by: Krzysztof Tchoń
MaRDI profile type: Publication
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OpenAlex ID: W2148385575
description: scientific article; zbMATH DE number 4097197