On periodic scheduling and control for networked systems under random data loss

This article deals with networked control systems (NCSs) whose shared networks have limited communication capacity and are prone to data losses. Our contributions are two-fold. First, we present necessary and sufficient conditions on the plant and controller dynamics and the network parameters such that there exist purely time-dependent periodic scheduling sequences under which the stability of each plant is preserved for all admissible data loss signals. Second, given a period for the scheduling sequence, we identify sufficient conditions on the plant dynamics and the network parameters such that the plants admit static state-feedback controllers that are favorable for the stability conditions presented. The main apparatus for our analysis is a switched system representation of the individual plants in an NCS whose switching signals are time-inhomogeneous Markov chains. Our stability conditions involve the existence of sets of symmetric and positive definite matrices that satisfy certain (in)equalities. We identify the existence of stabilizing periodic scheduling sequences and their corresponding favorable state-feedback controllers under ideal communication between the plants and their controllers as special cases of our results. A numerical experiment is presented to demonstrate the proposed techniques.