Pinning consensus in networks with time-varying topology and event-triggered diffusions via impulsive control

This paper studies pinning consensus of networks with time-varying topology via impulsive control. Event-triggered rules are employed in diffusion coupling terms to reduce the updating load of the coupled system. Sufficient conditions to pin the network to a prescribed value are proposed. It is proved that in case the coupling matrix across time intervals with length less than some given constant has spanning trees, then the proposed algorithms can realize consensus on the prescribed value when the impulsive controller is imposed randomly on one agent with appropriate impulsive strength and impulse intervals. The imposed pulses can be very sparse, with the impulsive intervals being lower bounded. Two kinds of event-triggered schemes coexist in this pinning control algorithm, one for updating the coupling diffusions; one for applying the impulsive control. Examples with numerical simulation are provided to show the effectiveness of the theoretical results.