ℓ2-ℓ∞ reliable control for discrete time-delay systems with saturated packet dropouts and stochastic nonlinearities

This paper deals with the ℓ₂-ℓ_∞ reliable control problem for a class of discrete time-delay systems. A sensor model is proposed to depict saturated packet dropouts which better reflect the reality in a networked environment. In addition, stochastic nonlinearities with statistical characteristics cover several well-studied nonlinear functions as special cases. The focus of this paper is placed upon the design of a reliable controller such that the closed-loop system satisfies a prescribed noise attenuation level in an ℓ₂-ℓ_∞ sense. By utilizing stochastic analysis methods, some sufficient conditions are established to guarantee both the exponentially mean-square stability and the ℓ₂-ℓ_∞ performance. Due to the obtained conditions with a nonlinear equality constraint, the cone complementary linearization method is exploited to cast them into a convex optimization 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.