Efficient techniques for solving the periodic projected Lyapunov equations and model reduction of periodic systems
type: Item
instance of: scholarly article
title: Efficient techniques for solving the periodic projected Lyapunov equations and model reduction of periodic systems
zbMATH Open document ID: 1426.93033
DOI: 10.1155/2017/4362641
author: Mohammad-Sahadet Hossain
author: M. Monir Uddin
published in: Mathematical Problems in Engineering
publication date: 2018-11-05T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 93B11
Mathematics Subject Classification ID: 65Q30
Mathematics Subject Classification ID: 65F30
zbMATH DE Number: 6972099
Wikidata QID: Q59147547
describes a project that uses: Periodic Systems Toolbox
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2017/4362641
OpenAlex ID: W2588142789
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description: scientific article; zbMATH DE number 6972099