Efficient Techniques for Solving the Periodic Projected Lyapunov Equations and Model Reduction of Periodic Systems
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 suc...
Saved in:
Published in | Mathematical problems in engineering Vol. 2017; no. 2017; pp. 1 - 11 |
---|---|
Main Authors | , |
Format | Journal Article |
Language | English |
Published |
Cairo, Egypt
Hindawi Publishing Corporation
01.01.2017
Hindawi Hindawi Limited |
Subjects | |
Online Access | Get full text |
Cover
Loading…
Summary: | 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. |
---|---|
Bibliography: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23 |
ISSN: | 1024-123X 1563-5147 |
DOI: | 10.1155/2017/4362641 |