A stochastic stability controller design for networked control systems with random time delays

For a class of the linear discrete-time networked control systems with both the sensor-to-controller and controller-to-actuator random time delays, state observers and stochastic stability controllers are designed in this paper. The random time delays are modeled as two Markov chain models. Based on Lyapunov stability theory and linear matrix inequalities, the necessary and sufficient conditions are derived for the existence of the state observers and the stochastic stability controllers. The state-observation gains and stochastic stability control gains are calculated via an iterative linear matrix inequality approach. A numerical example is provided to demonstrate the validity of the proposed design scheme.