Stabilization of Discrete-Time Networked Control Systems with Partly Known Transmission Delay: A New Augmentation Approach

This paper is concerned with the stabilization problem of discrete-time networked control systems with partly known transmission delay. Considering the random property of the networked-induced delay, the original system is transformed into a new delay model with stochastic parameter matrices by introducing a novel state augmentation technique. Based on the new model, a new delay-distribution-dependent criterion for the mean square stability of the closed-loop system is derived by using the Lyapunov-Krasovskii functional approach and linear matrix inequality technique. The solvability of the derived criterion depends on not only the size of the delay, but also the probability distribution of the delay taking value in a finite set. Finally, two numerical examples are given to demonstrate the effectiveness of the proposed method.