Matrix GPBiCG algorithms for solving the general coupled matrix equations

Linear matrix equations have important applications in control and system theory. In the study, we apply Kronecker product and vectorisation operator to extend the generalised product bi-conjugate gradient (GPBiCG) algorithms for solving the general coupled matrix equations ∑lj=1(A)i,1,jX1Bi,1,j+Ai,...

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Bibliographic Details
Published in:IET control theory & applications Vol. 9; no. 1; pp. 74 - 81
Main Author: Hajarian, Masoud
Format: Journal Article
Language:English
Published: The Institution of Engineering and Technology 02.01.2015
Subjects:
Algorithms
conjugate gradient methods
Control systems
control theory
coupled Markovian jump Lyapunov matrix equation
general coupled matrix equations
generalised product bi‐conjugate gradient
generalised Sylvester matrix equation
GPBiCG algorithm
Joining
Kronecker product
linear matrix equations
Markov processes
Mathematical analysis
Mathematical models
matrix algebra
Operators
system theory
Systems theory
vectorisation operator
conjugate gradient methods
generalised Sylvester matrix equation
control theory
coupled Markovian jump Lyapunov matrix equation
Kronecker product
generalised product bi-conjugate gradient
general coupled matrix equations
linear matrix equations
vectorisation operator
matrix algebra
GPBiCG algorithm
system theory
ISSN:1751-8644, 1751-8652
Online Access:Get full text
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Summary:Linear matrix equations have important applications in control and system theory. In the study, we apply Kronecker product and vectorisation operator to extend the generalised product bi-conjugate gradient (GPBiCG) algorithms for solving the general coupled matrix equations ∑lj=1(A)i,1,jX1Bi,1,j+Ai,2,jX2Bi,2,j+…+Ai,l,jXi,l,j) = Di  for  i = 1,2,…,l (including the (coupled) Sylvester, the second-order Sylvester and coupled Markovian jump Lyapunov matrix equations). We propose four effective matrix algorithms for finding solutions of the matrix equations. Numerical examples and comparison with other well-known algorithms demonstrate the effectiveness of the proposed matrix algorithms.
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ISSN:1751-8644
1751-8652
DOI:10.1049/iet-cta.2014.0669