Stabilization of linear discrete-time systems over resource-constrained networks under dynamical multiple description coding scheme

Abstract

In this paper, the stabilization problem is investigated for a class of linear discrete-time systems in a resource-constrained network environment where only the data with finite bits is permitted to transmit. The data transmissions from the sensors to the controller are subject to random packet dropouts. To improve the reliability of the data transmission, a novel dynamical multiple description coding scheme is developed with guaranteed convergence of the decoding error. By recurring to the matrix inequality theory and the stochastic analysis technique, sufficient conditions are established to ensure the stochastic stability of the closed-loop system. Furthermore, a parametric relationship is discovered that characterizes the influences from the packet-dropout probabilities and the encoder parameters on the stability of the closed-loop system. Finally, a numerical example is provided to illustrate the validity of the proposed control scheme.