Use of subsystems eigenstructures in dynamically interconnected systems for eigenvalue assignment
type: Item
instance of: scholarly article
title: Use of subsystems eigenstructures in dynamically interconnected systems for eigenvalue assignment
zbMATH Open document ID: 0536.93026
DOI: 10.1016/S0167-6911(84)80059-6
author: A. El-Kashlan
author: M. El-Geneidy
published in: Systems \& Control Letters
publication date: 1984-01-01T00:00:00Z
review text: An eigenvalue assignment problem is considered for a class of interconnected, discrete, linear dynamic systems. The problem reduces to one finding matrices R and N such that the matrix \[ \Gamma = \left[ \begin{matrix} A+BR & BN \\ LC & M \end{matrix} \right] \] has a given set of eigenvalues. A, B and C are block diagonal matrices describing the S subsystem: \(x_ r(k+1)=A_ rx_ r(k)+B_ ru(k)\), \(_ r(k)=C_ r(k),\quad r=1,...S,\) while N and M are block diagonal matrices describing the interconnections: \[ Z_ r(k+1)=M_ rZ_ r(k)+\sum^{s}_{q=1}L_{rq}y_ q(k),\quad U_ r(k)=N_ rZ_ r(k)+\sum^{s}_{q=1}R_{rq}x_ q(k) \] The main result: if, for \(r=1,...S\), (i) \((A_ r,B_ r)\) is controllable, (ii) \((L_ r,M_{rr})\) is controllable, (iii) the eigenvalues of A and of M are disjoint from those of the desired eigenvalues, then there exist matrices N and R which achieve the desired eigenvalues. The eigenstructures of the subsystem interconnections are exploited to achieve the desired eigenvalues, and an iterative scheme is proposed to solve the global problem.
Mathematics Subject Classification ID: 93B55
Mathematics Subject Classification ID: 93C05
Mathematics Subject Classification ID: 93C55
Mathematics Subject Classification ID: 93A15
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 93B40
zbMATH DE Number: 3852894
zbMATH Keywords: iterative coordination scheme
zbMATH Keywords: eigenvalue assignment
zbMATH Keywords: interconnected, discrete, linear dynamic systems
reviewed by: David A. Wilson
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3852894