Gradient based approach for generalized discrete-time periodic coupled Sylvester matrix equations

The paper is dedicated to solving the generalized periodic discrete-time coupled Sylvester matrix equation, which is frequently encountered in control theory and applied mathematics. The solvable condition and a iterative algorithm for this equation are presented. The proposed method is developed fr...

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Bibliographic Details
Published inJournal of the Franklin Institute Vol. 355; no. 15; pp. 7691 - 7705
Main Authors Lv, Lingling, Zhang, Zhe, Zhang, Lei, Liu, Xianxing
Format Journal Article
LanguageEnglish
Published Elmsford Elsevier Ltd 01.10.2018
Elsevier Science Ltd
Subjects
Applications of mathematics
Applied mathematics
Control theory
Discrete element method
Iterative algorithms
Iterative methods
Least squares method
Mathematical analysis
Matrix methods
Polynomials
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Summary:The paper is dedicated to solving the generalized periodic discrete-time coupled Sylvester matrix equation, which is frequently encountered in control theory and applied mathematics. The solvable condition and a iterative algorithm for this equation are presented. The proposed method is developed from a point of least squares method. The rationality of the method is testified by theoretical analysis, which shows that the algorithm can solve the problem within finite number of iterations. The presented approach is numerically reliable and requires less computation. A numerical example illustrates the effectiveness of the raised result.
ISSN:0016-0032
1879-2693
0016-0032
DOI:10.1016/j.jfranklin.2018.07.045