Gradient Based Iterative Algorithm to Solve General Coupled Discrete-Time Periodic Matrix Equations over Generalized Reflexive Matrices
The discrete-time periodic matrix equations are encountered in periodic state feedback problems and model reduction of periodic descriptor systems. The aim of this paper is to compute the generalized reflexive solutions of the general coupled discrete-time periodic matrix equations. We introduce a g...
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| Vydáno v: | Mathematical modelling and analysis Ročník 21; číslo 4; s. 533 - 549 |
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| Médium: | Journal Article |
| Jazyk: | angličtina |
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Vilnius Gediminas Technical University
23.06.2016
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| ISSN: | 1392-6292, 1648-3510 |
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| Abstract | The discrete-time periodic matrix equations are encountered in periodic state feedback problems and model reduction of periodic descriptor systems. The aim of this paper is to compute the generalized reflexive solutions of the general coupled discrete-time periodic matrix equations. We introduce a gradient-based iterative (GI) algorithm for finding the generalized reflexive solutions of the general coupled discretetime periodic matrix equations. It is shown that the introduced GI algorithm always converges to the generalized reflexive solutions for any initial generalized reflexive matrices. Finally, two numerical examples are investigated to confirm the efficiency of GI algorithm. |
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| AbstractList | The discrete-time periodic matrix equations are encountered in periodic state feedback problems and model reduction of periodic descriptor systems. The aim of this paper is to compute the generalized reflexive solutions of the general coupled discrete-time periodic matrix equations. We introduce a gradient-based iterative (GI) algorithm for finding the generalized reflexive solutions of the general coupled discretetime periodic matrix equations. It is shown that the introduced GI algorithm always converges to the generalized reflexive solutions for any initial generalized reflexive matrices. Finally, two numerical examples are investigated to confirm the efficiency of GI algorithm. The discrete-time periodic matrix equations are encountered in periodic state feedback problems and model reduction of periodic descriptor systems. The aim of this paper is to compute the generalized reflexive solutions of the general coupled discrete-time periodic matrix equations. We introduce a gradient-based iterative (GI) algorithm for finding the generalized reflexive solutions of the general coupled discretetime periodic matrix equations. It is shown that the introduced GI algorithm always converges to the generalized reflexive solutions for any initial generalized reflexive matrices. Finally, two numerical examples are investigated to confirm the efficiency of GI algorithm.Keywords: discrete-time periodic matrix equation, iterative algorithm, gradient based iterative algorithm, generalized reflexive solution .AMS Subject Classification: 15A24; 39B42; 65F10; 65F30. |
| Audience | Academic |
| Author | Hajarian, Masoud |
| Author_xml | – sequence: 1 givenname: Masoud surname: Hajarian fullname: Hajarian, Masoud organization: Department of Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, General Campus, Evin, 19839 Tehran, Iran |
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| CitedBy_id | crossref_primary_10_1007_s10898_018_0692_4 crossref_primary_10_1007_s11075_018_0553_8 crossref_primary_10_1016_j_camwa_2018_03_020 crossref_primary_10_1108_EC_11_2023_0788 crossref_primary_10_1016_j_jfranklin_2022_07_051 crossref_primary_10_1002_oca_3134 crossref_primary_10_1007_s12190_020_01486_6 crossref_primary_10_1186_s13662_019_2036_1 crossref_primary_10_1177_0142331216670719 crossref_primary_10_3934_jimo_2025076 crossref_primary_10_1016_j_jfranklin_2018_02_014 crossref_primary_10_1002_asjc_1528 |
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| Keywords | generalized reflexive solution gradient based iterative algorithm discrete-time periodic matrix equation iterative algorithm |
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| SubjectTerms | Algorithms discrete-time periodic matrix equation generalized reflexive solution gradient based iterative algorithm iterative algorithm Mathematical research Matrices (Mathematics) |
| Title | Gradient Based Iterative Algorithm to Solve General Coupled Discrete-Time Periodic Matrix Equations over Generalized Reflexive Matrices |
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