Round-robin temporal scheduling of exponentially stabilizing controllers

We study the behavior of a control-affine nonlinear system under periodic switching of the active control channel. The periodic switching between the control channels is implemented in a round-robin fashion. We claim that if a globally exponentially stabilizing feedback controller is sparsified using the round-robin scheme and the control action to each channel is scaled appropriately, then the resulting system is stabilized. For numerical proof of concept, we illustrate the effect of such sparsification on a linearized model of a coupled inverted pendulum - simple harmonic oscillator system.