ℓ 2 –ℓ ∞ reliable control for discrete time‐delay systems with fractional uncertainties and saturated package losses

Abstract

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.