On some aspects of observability of stochastic systems
type: Item
instance of: scholarly article
zbMATH Open document ID: 1058.93016
DOI: 10.1023/A:1009684600435
publication date: 2000-01-01T00:00:00Z
Mathematics Subject Classification ID: 93B07
Mathematics Subject Classification ID: 93E03
Mathematics Subject Classification ID: 37H10
Mathematics Subject Classification ID: 93B28
zbMATH DE Number: 1658675
zbMATH Keywords: stochastic observability
zbMATH Keywords: semigroups of linear operators
zbMATH Keywords: Chebyshev systems
zbMATH Keywords: Hessenberg generator
author: Andrzej Jamiołkowski
MaRDI profile type: Publication
full work available at URL: a:1009684600435
OpenAlex ID: W1720129703
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published in: Open Systems \& Information Dynamics
title: On some aspects of observability of stochastic systems
review text: Different aspects of stochastic observability of dynamical systems described by semigroups of linear operators are discussed. First, basic notions taken from the theory of linear operators and semigroups are presented. Next, using methods of functional analysis, necessary and sufficient conditions for stochastic observability are formulated and proved. The problem of minimization of the number of measurements needed for stochastic observability is discussed with the aid of linear algebra methods. The minimal number of moments of observations are estimated. Finally, observability of Chebyshev systems is considered and an effevtive method for its investigation is proposed. Observability of systems with the so-called Hessenberg generator is also considered.NEWLINENEWLINE In addition the paper contains several remarks and comments concerning stochastic observability, and its connections with stochastic controllability are also presented. The relationships to the results on stochastic observability given in the literature are mentioned. The stochastic dynamical systems considered in the paper can also be found in the monograph [\textit{R. S. Ingarden}, \textit{A. Kossakowski} and \textit{M. Ohya}, Information dynamics and open systems (Kluwer Academic Publishers, Dordrecht) (1997; Zbl 0891.94007)].
reviewed by: Jerzy Klamka
description: scientific article; zbMATH DE number 1658675