Simultaneous stability of a collection of networked control systems with uncertain delays

This paper is concerned with simultaneous stability of a collection of continuous-time linear plants whose feedback control loops are closed via a shared digital communication network. Because of the limitation of communication capacity, only a limited number of controller-plant connections can be accommodated at any time instant. Therefore, it is necessary to carefully design the scheduling policy so as to achieve simultaneous stabilization for all these control loops. In the paper, sufficient condition on the existence of such a scheduling policy is presented for the collection of networked LTI systems with sampled-data controllers and network-induced uncertain delays. It turns out that the condition is only based on the convergence rate of the closed-loop system and the divergence rate of the open-loop plant. The proof for this schedulability condition is in a constructive way, which can also serve as a systematic way for the scheduling policy design.