Observer-based H∞ control of two-dimensional delayed networks under the random access protocol

Abstract In this paper, the H∞ control problem is investigated for a time-delayed two-dimensional (2-D) network under the random access protocol (RAP). The control input is transmitted to the actuator via a network with communication constraint, where only one signal obtains the network access at each transmission instant, and the RAP is adopted here to schedule the data transmission which is depicted by an independent and identically distributed sequence. The randomly occurring uncertainty, nonlinearity and unknown time delays are all introduced in the underlying 2-D system. The aim of the addressed problem is to design an observer-based controller so that the considered 2-D system has a predefined H∞ performance index. Sufficient condition is given to ensure the H∞ performance of the closed-loop system via the Lyapunov theory and stochastic analysis. Moreover, the observer-based controller is dexterously designed to ensure the achievement of the H∞ performance, under which the controller gains are designed by solving certain matrix inequalities. Finally, a numerical example is given to demonstrate effectiveness of the proposed approach.