Solution Bounds and Numerical Methods of the Unified Algebraic Lyapunov Equation
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Published:2022-08-11
Issue:16
Volume:10
Page:2858
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ISSN:2227-7390
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Container-title:Mathematics
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language:en
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Short-container-title:Mathematics
Author:
Zhang Juan,Li Shifeng,Gan Xiangyang
Abstract
In this paper, applying some properties of matrix inequality and Schur complement, we give new upper and lower bounds of the solution for the unified algebraic Lyapunov equation that generalize the forms of discrete and continuous Lyapunov matrix equations. We show that its positive definite solution exists and is unique under certain conditions. Meanwhile, we present three numerical algorithms, including fixed point iterative method, the acceleration fixed point method and the alternating direction implicit method, to solve the unified algebraic Lyapunov equation. The convergence analysis of these algorithms is discussed. Finally, some numerical examples are presented to verify the feasibility of the derived upper and lower bounds, and numerical algorithms.
Funder
National Natural Science Foundation of China
Natural Science Foundation for Distinguished Young Scholars of Hunan 173 Province
Subject
General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)
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