Stabilization of networked multi-input systems over AWGN channels with channel resource allocation

In this paper, we study stabilization of multi-input networked control systems over additive white Gaussian noise channels. Different from the single-input case, which is available in the literature and boils down to a typical ℋ₂ optimal control problem, the multi-input case involves a judicious allocation of the total capacity among the input channels in addition to the design of the feedback controller. With this channel-controller co-design, we successfully show that a networked multi-input system over additive white Gaussian noise channels can be stabilized by state feedback under channel resource allocation, if and only if the total channel capacity is greater than the topological entropy of the plant. A numerical example is given to demonstrate our result.