PDdE-based analysis of vehicular platoons with spatio-temporal decoupling

The paper provides exact analytical solutions of wave-like PDdE-based (partial differential-difference equation) models of several popular vehicular platooning problems with bidirectional distributed control. Efficient evaluation of eigenvalues, eigenfunctions and wave velocities is proposed for a finite vehicular platoon without an approximation by a continuum model. Thanks to the decoupling of spatial and temporal dynamics, closed-loop stability can be analyzed by looking at a characteristic polynomial using a root-locus-like graphical technique. Although the paper only contains discussions for static state feedback controllers (using measurements of inter-vehicular distances and relative velocities), extensiona to higher-order (dynamic) controllers is straighforward and will be included in the extended version of the paper.