Abstract

An earlier investigation on a leaderless consensus protocol for double integrators with multiple time delays (Meng et al., 2011) 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 stability tables for the dynamics in the space of the delays. Furthermore they are exact and exhaustive. 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. Examples cases are provided to display the strengths, efficiency and explicitness of this new stability analysis mechanism.

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