Networked Stabilization of Multi-Input Discrete Systems With Multiplicative Noise

This paper studies the mean square stabilization problem of multi-input discrete-time systems with multiplicative noise constraints. The channel resources are fixed and cannot be arbitrarily allocated, and the channel is modeled as multiplicative noise. The main purpose is to discuss the relationship between the minimum channel capacity of each subchannel and the system topological entropy by using majorization theory. The basic idea is to investigate the stabilization from the perspective of the supply and demand balance. Specifically, for communication resources, each system input is regarded as the demand side and the channel is considered as the supplier. The supply resources of the channel are characterized according to the channel capacity, and stabilization of networked control systems requires a balance between the supply and demand of the communication resources. Since the channel resources are not configurable, one can satisfy the supplier’s requirements by adjusting the demand side (a certain transmission mechanism). We provide a sufficient condition and a necessary condition to stabilize networked control systems. Finally, numerical examples verify the conclusions.

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