Time Parameters Shape the Controllability of Temporally Switching Networks

Abstract

Based on temporally switching networks, this work studies the influence of time parameters on network controllability. In particular, this work presents a necessary and sufficient condition under which the network controllability must take into account time parameters. For the time parameters that never participate in determining network controllability, a more concise expression of controllability criterion is derived. From the perspective of input matrix formulation, this work also presents a sufficient condition under which the network controllability could avoid the interference of time parameters. By taking control energy as the quantitative measurement, the increase in time parameter would decrease the lower bound of minimum control energy. However, the increase in time parameter may cause an upsurge in the upper bound of minimum control energy. In addition, we find that there exists a statistically significant correlation between time parameter influence level and network characteristic. This work highlights for the first time that subtle changes in time parameters could reshape or even worsen the controllability of temporally switching networks.