Open AccessImplicit iterative algorithms with a tuning parameter for discrete stochastic Lyapunov matrix equations
Author(s) -
Zhang Ying,
Wu AiGuo,
Shao ChunTao
Publication year - 2017
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.2016.1601
Subject(s) - mathematics , convergence (economics) , multiplicative noise , lyapunov function , matrix (chemical analysis) , monotonic function , iterative method , algorithm , mathematical optimization , computer science , nonlinear system , transmission (telecommunications) , mathematical analysis , telecommunications , physics , materials science , signal transfer function , quantum mechanics , analog signal , economics , composite material , economic growth
An implicit iterative algorithm is established for solving a class of Lyapunov matrix equations appearing in the discrete‐time stochastic systems with multiplicative noise. This algorithm contains a tuning parameter which can be appropriately chosen such that it has better convergence performance. Some convergence conditions have been derived for the proposed iterative algorithm, and for a special case an approach is given to choose the optimal tuning parameter such that the algorithm has the best convergence performance. In addition, the properties of boundedness and monotonicity of the proposed algorithm are also investigated when the corresponding stochastic system is asymptotically mean‐square stable.