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Efficient Techniques for Solving the Periodic Projected Lyapunov Equations and Model Reduction of Periodic Systems
Joint Authors
Hossain, Mohammad-Sahadet
Uddin, M. Monir
Source
Mathematical Problems in Engineering
Issue
Vol. 2017, Issue 2017 (31 Dec. 2017), pp.1-11, 11 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2017-02-14
Country of Publication
Egypt
No. of Pages
11
Main Subjects
Abstract EN
We have presented the efficient techniques for the solutions of large-scale sparse projected periodic discrete-time Lyapunov equations in lifted form.
These types of problems arise in model reduction and state feedback problems of periodic descriptor systems.
Two most popular techniques to solve such Lyapunov equations iteratively are the low-rank alternating direction implicit (LR-ADI) method and the low-rank Smith method.
The main contribution of this paper is to update the LR-ADI method by exploiting the ideas of the adaptive shift parameters computation and the efficient handling of complex shift parameters.
These approaches efficiently reduce the computational cost with respect to time and memory.
We also apply these iterative Lyapunov solvers in balanced truncation model reduction of periodic discrete-time descriptor systems.
We illustrate numerical results to show the performance and accuracy of the proposed methods.
American Psychological Association (APA)
Hossain, Mohammad-Sahadet& Uddin, M. Monir. 2017. Efficient Techniques for Solving the Periodic Projected Lyapunov Equations and Model Reduction of Periodic Systems. Mathematical Problems in Engineering،Vol. 2017, no. 2017, pp.1-11.
https://search.emarefa.net/detail/BIM-1190408
Modern Language Association (MLA)
Hossain, Mohammad-Sahadet& Uddin, M. Monir. Efficient Techniques for Solving the Periodic Projected Lyapunov Equations and Model Reduction of Periodic Systems. Mathematical Problems in Engineering No. 2017 (2017), pp.1-11.
https://search.emarefa.net/detail/BIM-1190408
American Medical Association (AMA)
Hossain, Mohammad-Sahadet& Uddin, M. Monir. Efficient Techniques for Solving the Periodic Projected Lyapunov Equations and Model Reduction of Periodic Systems. Mathematical Problems in Engineering. 2017. Vol. 2017, no. 2017, pp.1-11.
https://search.emarefa.net/detail/BIM-1190408
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1190408