Robust H ∞ state feedback control of NCSs with Poisson noise and successive packet dropouts

Abstract

This paper examines various constraints of networked control systems (NCSs) such as network-induced random delays, successive packet dropouts and Poisson noise. Time delays are represented as modes of Markov chain and successive packet dropouts are modeled using Poisson probability distribution. For each delay-mode, a separate Poisson distribution is used with the help of an indicator function. Poisson noise is incorporated in the design to cater sudden network link failures and power shutdowns. After modeling these constraints, a stability criterion is proposed by using Lyapunov-Krasovskii functional. On the basis of the stability criteria, sufficient conditions for the existence of a robust H ∞ state feedback controller are given in terms of bilinear matrix inequalities (BMIs). Later, BMIs are converted into quasi-convex linear matrix inequalities (LMIs) and are solved by using a cone complementarity linearizing algorithm. The effectiveness of the proposed scheme is elaborated with the help of two simulation examples. Moreover, the effects of successive packet dropouts and Poisson noise on H ∞ performance are analyzed.