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Designing a Continuous Reconstruction Operator in Observation Problems for Ordinary Linear Systems

Designing a Continuous Reconstruction Operator in Observation Problems for Ordinary Linear Systems Differential Equations, Vol. 39, No. 3, 2003, pp. 362–368. Translated from Differentsial'nye Uravneniya, Vol. 39, No. 3, 2003, pp. 337–342. Original Russian Text Copyright c 2003 by Metel'skii, Minyuk. ORDINARY DIFFERENTIAL EQUATIONS Designing a Continuous Reconstruction Operator in Observation Problems for Ordinary Linear Systems A. V. Metel'skii and S. A. Minyuk Belarus State Technical University, Minsk, Belarus Grodno State University, Grodno, Belarus Received February 1, 2002 INTRODUCTION Consider the observation system x _ (t)= A(t)x(t);t 2 T =[t ;t ]; (1) 0 1 with output y(t)= c(t)x(t);t 2 T; (2) where A(t)is an n n matrix and c(t)is a row n-vector with continuous entries on T . There are two approaches to the statement of the observation problem for system (1), (2). The rst approach assumes [1, p. 68 of the Russian translation; 2, p. 188] a one-to-one correspon- dence between the set of initial states x (t )= x and the set of outputs 0 0 y(t)= y t;x = c(t)x t;t ;x ;t 2 T; 0 0 where x (t;t ;x ) is the solution of the vector equation (1) with the initial condition x (t )= x . 0 0 The second approach, suggested in [3], http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations Springer Journals

Designing a Continuous Reconstruction Operator in Observation Problems for Ordinary Linear Systems

Metel'skii, A.; Minyuk, S.
Differential Equations , Volume 39 (3) – Oct 5, 2004
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References (2)

Publisher
Springer Journals
Copyright
Copyright © 2003 by MAIK “Nauka/Interperiodica”
Subject
Mathematics; Difference and Functional Equations; Ordinary Differential Equations; Partial Differential Equations
ISSN
0012-2661
eISSN
1608-3083
DOI
10.1023/A:1026069617754
Publisher site
See Article on Publisher Site

Abstract

Differential Equations, Vol. 39, No. 3, 2003, pp. 362–368. Translated from Differentsial'nye Uravneniya, Vol. 39, No. 3, 2003, pp. 337–342. Original Russian Text Copyright c 2003 by Metel'skii, Minyuk. ORDINARY DIFFERENTIAL EQUATIONS Designing a Continuous Reconstruction Operator in Observation Problems for Ordinary Linear Systems A. V. Metel'skii and S. A. Minyuk Belarus State Technical University, Minsk, Belarus Grodno State University, Grodno, Belarus Received February 1, 2002 INTRODUCTION Consider the observation system x _ (t)= A(t)x(t);t 2 T =[t ;t ]; (1) 0 1 with output y(t)= c(t)x(t);t 2 T; (2) where A(t)is an n n matrix and c(t)is a row n-vector with continuous entries on T . There are two approaches to the statement of the observation problem for system (1), (2). The rst approach assumes [1, p. 68 of the Russian translation; 2, p. 188] a one-to-one correspon- dence between the set of initial states x (t )= x and the set of outputs 0 0 y(t)= y t;x = c(t)x t;t ;x ;t 2 T; 0 0 where x (t;t ;x ) is the solution of the vector equation (1) with the initial condition x (t )= x . 0 0 The second approach, suggested in [3],

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Differential Equations – Springer Journals

Published: Oct 5, 2004

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