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Mean Square Stabilization of Multi-Input Discrete-Time Systems Over Stochastic Multiplicative and Additive White Gaussian Noise Channels

This paper studies mean square stabilization for multi-input discrete-time systems over a general fading channel, and the channel is modeled as a cascade of multiplicative noise and white Gaussian additive noise. The main objective is to determine the minimum mean capacity required to enable stabilization. The basic idea of our method is to consider stabilization from the viewpoint of a supply/demand balance. Specifically, for communication resources, each system control input is viewed as the demand side, while the channel is viewed as the supply side, and the supply resource of the channel is characterized by the mean square capacity of each channel. Stabilization of the networked control system requires the balance of supply and demand. Based on whether the channel resources are configurable, two different methods for balancing the supply and the demand are discussed. If the channel resources are configurable, the demand side can be satisfied by adjusting the supply side (channel resources); otherwise, the demand side (a certain transceiver design mechanism) can be adjusted to meet the requirements of the supplier. For both cases, sufficient and necessary conditions for stabilizing discrete-time networked control systems are given.