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Observer‐based H ∞ control of discrete Markovian jump delay systems with random packet losses and multiplicative noises
Author(s) -
Wen Shiping,
Zeng Zhigang,
Huang Tingwen,
Bao Gang
Publication year - 2012
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.2054
Subject(s) - control theory (sociology) , multiplicative function , multiplicative noise , observer (physics) , bernoulli's principle , bernoulli distribution , network packet , mathematics , controller (irrigation) , computer science , random variable , control (management) , transmission (telecommunications) , statistics , mathematical analysis , engineering , physics , telecommunications , computer network , agronomy , signal transfer function , quantum mechanics , artificial intelligence , analog signal , biology , aerospace engineering
SUMMARY This paper investigates the observer‐based H ∞ control problem for a class of mixed‐delay Markovian jump systems with random communication packet losses and multiplicative noises. The mixed delays comprise both discrete time‐varying delays and distributed delays, the random packet losses are described by a Bernoulli distributed white sequence that obeys a conditional probability distribution, and the multiplicative disturbances are in the form of a scalar Gaussian white noise with unit variance. In the presence of mixed delays, random packet losses and multiplicative noises, sufficient conditions for the existence of an observer‐based feedback controller are derived such that the closed‐loop control system is asymptotically mean‐square stable and preserves a guaranteed H ∞ performance. Then, a linear matrix inequality approach for designing such an observer‐based H ∞ controller is presented. Finally, a numerical example is provided to illustrate the effectiveness of the developed theoretical results. Copyright © 2012 John Wiley & Sons, Ltd.