Robust mode delay-dependent H∞ control of discrete-time systems with random communication delays

This study considers stability and robust mode delay-dependent ℋ_∞ controller design for discrete-time systems with random communication delays. Communication delays between sensors and controllers are modelled by a finite state Markov process. Based on Lyapunov-Krasovskii functional, a novel methodology for designing a mode delay-dependent state feedback controller has been proposed. The authors also show that the existing delay-dependent approach is a special case of the mode delay-dependent approach proposed in this study. The mode delay-dependent controller is obtained by solving linear matrix inequality optimisation problems using the cone complementarity linearisation algorithm. The effectiveness of the proposed design methodology is verified by a numerical example.