State observers for linear systems with uncertainty
type: Item
instance of: scholarly article
title: State observers for linear systems with uncertainty
zbMATH Open document ID: 1225.93001
DOI: 10.1515/9783110218138
author: S. K. Korovin
author: V. V. Fomichev
published in: De Gruyter Expositions in Mathematics
publication date: 2009-11-10T00:00:00Z
review text: The book presents the latest achievements in the field of synthesis of asymptotic state observers for dynamical systems described by linear ordinary differential equations or by their discrete-time analogues. Chapter 1 contains the statement of the problem of constructing of a state observer, notions of the asymptotic and finite observers, and notions of the minimal and functional observers. In Chapter 2, the concepts of observability and identifiability are considered for linear dynamical systems of the form \[ \dot{x}=A(t)x+B(t)u, \qquad y=C(t)x, \] where \(x \in \mathbb R^n\) is an unknown state (phase) vector, \(u \in \mathbb R^m\), \(y \in \mathbb R^l\), are known input and output, respectively. Kalman's and Rosenbrock's observability criteria are given for linear stationary systems, and also some canonical forms are described. Chapter 3 presents algorithms of synthesis of full-dimensional state observers for scalar and vector stationary fully determined systems. In Chapter 4, the authors describe new approaches to the synthesis of functional observers of the given order for fully determined systems. They propose an algorithm for synthesizing functional observers of minimal order and obtain lower bounds for the order of the observers. Chapter 5 deals with the problem of asymptotic observers synthesis for linear stationary systems with unknown disturbances \(Df\) in the right-hand part of the state equation. For hyper-output systems two approaches to solving the problem are proposed, namely, the method of quasisplitting and the methods of pseudoinputs. For square systems an approach is proposed which makes it possible to obtain an estimate of the unknown state vector with any preassigned accuracy, but this approach is not asymptotic. In Chapter 6, the observer constructing problem is analyzed for the class of stationary dynamical systems with bilinear term \(uBx\) in the right-hand part of the state equation. Planar (\(x \in \mathbb R^2\)) bilinear systems are c…
Mathematics Subject Classification ID: 93-02
Mathematics Subject Classification ID: 93B07
Mathematics Subject Classification ID: 93C55
zbMATH DE Number: 5628240
zbMATH Keywords: control theory
zbMATH Keywords: observability
zbMATH Keywords: asymptotic observer
zbMATH Keywords: functional observer
zbMATH Keywords: minimal observer
zbMATH Keywords: systems with uncertainty
zbMATH Keywords: discrete-time systems
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1515/9783110218138
OpenAlex ID: W644925237
description: scientific article; zbMATH DE number 5628240