Exact stability analysis of second-order leader-follower consensus protocols with multiple time delays

An earlier investigation on leader-follower consensus protocols for double integrators with multiple time delays [1] is revisited in this paper from two completely different and novel perspectives. First, the crucial stability analysis of time delayed system is replaced with a recent technique called the Cluster Treatment of Characteristic Roots (CTCR). CTCR paradigm is pursued after a block-diagonalization (mode decoupling) transformation on the system. This treatment produces the unique exact and exhaustive stability tables for the dynamics in the space of the delays. Secondly, the novel concept of Spectral Delay Space is presented, as an overture to the CTCR for the determination of the needed potential stability crossing (switching) hypersurfaces in the delay space. Example cases are provided to display the strengths, efficiency and explicitness of this new stability analysis mechanism.