Open AccessCurrent‐estimation‐based iterative algorithms for solving periodic Lyapunov matrix equations
Author(s) -
Wu AiGuo,
Chang MingFang
Publication year - 2016
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/iet-cta.2015.1313
Subject(s) - mathematics , lyapunov function , lyapunov equation , matrix (chemical analysis) , monotonic function , algorithm , iterative method , current (fluid) , control theory (sociology) , mathematical optimization , computer science , lyapunov exponent , nonlinear system , chaotic , mathematical analysis , control (management) , physics , materials science , quantum mechanics , artificial intelligence , composite material , electrical engineering , engineering
In this study, two novel iterative algorithms are presented to solve the Lyapunov matrix equations appearing in discrete‐time periodic linear systems. In both algorithms, a weighted combination of the estimation in the last and the current steps is used to update the estimation of the unknown matrices. It is shown that the sequences generated by the proposed algorithms with zero initial conditions monotonically converge to the unique positive definite solution of the periodic Lyapunov matrix equation if the associated system is asymptotically stable. Finally, a numerical example is used to illustrate the effectiveness of the proposed algorithms.