Observability of quasimonotonic systems
type: Item
instance of: scholarly article
title: Observability of quasimonotonic systems
zbMATH Open document ID: 0653.93009
author: B. G. Zaslavskij
published in: Automation and Remote Control
publication date: 1987-01-01T00:00:00Z
review text: Consider the plant \(\dot x=F(x)\), \(x\in R^ m\), \(y=H(x)\), \(y\in R^ p\), where F, H are continuously differentiable with \(F(0)=0\), \(H(0)=0\), and F is quasimonotonic (i.e. \(\partial F_ i/\partial x_ j\geq 0\), \(i\neq j)\). The paper deals with the construction of an operator G: \({\mathcal L}\to R^ m\) (\({\mathcal L}\) denotes a vector space of functions of a scalar argument that take their values in \(R^ p)\) which in the case of an undistorted signal y(t) exactly reproduces x(t). In the case of bounded noise which distorts y(t) it yields minimum observation error, and in the case when y(t) belongs to the nonnegative (positive) cone of \({\mathcal L}\) it yields nonnegative (positive) solutions. When F is unknown the author proposes the following approach (dynamic observation): using a plant model \(\dot z=F_ 0(z,u)\), \(z\in R^ m\), \(u\in R^ p\), realized on a computer, one has to design the control u in order to achieve z(t)\(\to x(t)\) asymptotically. An illustrative example is finally given.
Mathematics Subject Classification ID: 93B07
Mathematics Subject Classification ID: 47H05
Mathematics Subject Classification ID: 93C10
Mathematics Subject Classification ID: 60G35
Mathematics Subject Classification ID: 93E10
zbMATH DE Number: 4066712
zbMATH Keywords: quasimonotonic systems
zbMATH Keywords: minimum observation error
zbMATH Keywords: nonnegative (positive) solutions
zbMATH Keywords: dynamic observation
reviewed by: Mihail Voicu
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4066712