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Robust reliable control for discrete‐time‐delay systems with stochastic nonlinearities and multiplicative noises
Author(s) -
Liu Yisha,
Wang Zidong,
Wang Wei
Publication year - 2011
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.938
Subject(s) - control theory (sociology) , nonlinear system , multiplicative function , discrete time and continuous time , multiplicative noise , mathematics , actuator , scalar (mathematics) , computer science , control (management) , transmission (telecommunications) , statistics , mathematical analysis , telecommunications , physics , signal transfer function , quantum mechanics , artificial intelligence , analog signal , geometry
This paper is concerned with the reliable control problem against actuator failures for a class of uncertain discrete‐time stochastic nonlinear time‐delay systems. The failures of actuators are quantified by a variable varying in a given interval. The stochastic nonlinearities described by statistical means cover several well‐studied nonlinear functions as special cases. The time‐varying delay is unknown with given lower and upper bounds. The multiplicative stochastic disturbances are in the form of a scalar Gaussian white noise with unit variance. Attention is focused on the analysis and design of a stable controller such that, for all possible actuator failures, stochastic nonlinearities and disturbances, time delays and admissible parameter uncertainties, the closed‐loop system is exponentially mean‐square stable. A linear matrix inequality approach is developed to solve the addressed problem. A numerical example is given to demonstrate the effectiveness of the proposed design approach. Copyright © 2010 John Wiley & Sons, Ltd.