Stability analysis and controller design for networked control systems with random time delay

This article deals with the problem of stabilisation for a class of networked control systems with random time delay via the state feedback control. The transmission delay is modelled as a Markov process, and the resulting closed-loop system is modelled as a Markovian jump linear system. Based on the Lyapunov stability theorem combined with linear matrix inequality (LMI) techniques, some new delay-dependent stochastic stability criteria for the system are derived. A switching state feedback controller that makes the closed-loop system stochastically stable is designed, which is obtained by solving some LMIs. Numerical simulation results illustrate the effectiveness of the method proposed in this article.