Discretization-based stabilization for a class of switched linear systems with communication delays

The stabilization problem for a class of switched linear systems is investigated in the network environment. Both the synchronous and asynchronous cases are considered according to the availability of the current activated system mode to the actuator. The random communication delay is assumed to be Markovian, resulting in a sampled-data synchronous or asynchronous switched system with Markovian delay as the closed-loop system. We extend the discretization approach to deal with such sampled-data system through exploring the stability conditions of the corresponding discrete-time system. For the asynchronous case, we formulate the closed-loop system as a hybrid system with the switching between its subsystems governed by a switching signal and a Markov chain. By studying the switching number and one-step reachable mode set of the constructed vector-valued switching signal, the exponential mean-square stability (EMSS) conditions and the corresponding mode-dependent controller are obtained with a more general constraint on the designed switching signal. These results are finally verified by two illustrated numerical examples.