Simultaneously Stabilizing Networked Systems with Minimal Communication

Self-triggered feedback control is used as a means to reduce the energy and communication requirements of networked systems. Triggered-control schemes result in aperiodic communications, with a potential for communication conflicts when multiple feedback loops are closed over a shared network. In this paper, we analyze the necessary/sufficient conditions for simultaneous stabilizability of a set of nonlinear systems over a network from the perspective of scheduling theory, using Lyapunov functions and input to state stability. We then propose a recursively feasible self-triggering scheme that minimizes the usage of the communication channel while ensuring the stability of all systems.