Open Accessℓ 2 –ℓ ∞ reliable control for discrete time‐delay systems with fractional uncertainties and saturated package losses
Author(s) -
Li Zhen'na,
Shu Huisheng,
Kan Xiu
Publication year - 2014
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.2013.0987
Subject(s) - control theory (sociology) , control (management) , discrete time and continuous time , mathematics , computer science , statistics , artificial intelligence
This study deals with the ℓ 2 –ℓ ∞ reliable control problem for a class of discrete time‐delay systems. The considered system involves fractional uncertainties, saturated package losses and stochastic non‐linearities as well as possible actuator failures. A sensor model is proposed to depict the phenomenon of saturated package losses which better reflect the reality in a networked environment. In addition, stochastic non‐linearities with statistical characteristics cover several well‐studied non‐linear functions as special cases. The focus of this study is placed upon the design of a reliable controller such that the closed‐loop system satisfies a prescribed noise attenuation level in an ℓ 2 –ℓ ∞ sense. By utilising stochastic analysis methods, some sufficient conditions are established to guarantee both the exponentially mean‐square stability and the ℓ 2 –ℓ ∞ performance. Owing to the obtained conditions with a non‐linear equality constraint, the cone complementary linearisation method is exploited to cast them into a convex optimisation problem, which can be readily solved by using standard numerical software. Finally, a simulation example is exploited to demonstrate the applicability of the proposed design approach.