Harmonic instability of asymmetric bidirectional control of a vehicular platoon

This paper deals with harmonic instability of asymmetric control of vehicular platoons. The considered platoons are composed of identical linear models of arbitrary order but there must be at least two integrators in the open loop. Each vehicle only responds to the movement of its immediate neighbors—the predecessor and the follower—and these two couplings are nonidentical. We show that for arbitrary asymmetry of intervehicular coupling, there is an exponential growth of the peak in the platoon's magnitude frequency responses as the number of vehicles grows—a phenomenon called harmonic instability in the literature. Whereas it has been already shown for some particular cases that the beneficial effects of having the Laplacian eigenvalues lower-bounded by a nonzero constant come at the cost of harmonic instability, here we generalize this result to any linear controllers.