Open AccessLinear minimum mean‐square estimation for discrete‐time measurement‐delay systems with multiplicative noise and Markov jump
Author(s) -
Song Xinmin,
Park Ju H.
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.2015.1197
Subject(s) - mathematics , multiplicative noise , estimator , ergodicity , markov chain , riccati equation , multiplicative function , control theory (sociology) , lyapunov function , minimum mean square error , mathematical analysis , differential equation , statistics , computer science , nonlinear system , physics , control (management) , signal transfer function , digital signal processing , artificial intelligence , analog signal , quantum mechanics , computer hardware
This study addresses the estimation problem for discrete‐time measurement‐delay systems with multiplicative noise and Markov jump. First, the state equation is converted into two equations according to the geometric arguments and flexible transformations. Then, based on the reorganised innovation approach, the finite‐horizon linear minimum mean‐square‐error estimator is derived in terms of two Riccati difference equations and two Lyapunov difference equations. Finally, under the assumptions of mean square stability of the system and ergodicity of the associated Markov chain, a sufficient condition for the existence of the infinite‐horizon estimator is presented. We provide a numerical example to manifest the efficiency of the proposed approach.