Stabilization of descriptor systems over networks with random communication delays

This paper addresses the stabilization problem of discrete-time descriptor systems over networks with random communication delays. By modeling the sensor-to-controller and controller-to-actuator delays as Markovian chains, the closed-loop system can be expressed as a jump linear descriptor system with two modes. The stochastically admissible necessary and sufficient condition for closed-loop system is constructed. An explicit expression for the desired controller is given without any system decomposition. The obtained results are formulated in terms of strict LMIs. In addition, an example is given to illustrate the effectiveness of the proposed approach.