Exact stability analysis of second-order leaderless and leader–follower consensus protocols with rationally-independent multiple time delays
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2013-04-13
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Abstract
An investigation of double-integrator agents with directed asymmetric consensus protocols and multiple
rationally independent time delays is presented in this paper from two novel perspectives. First, we
complement the group consensus literature on crucial stability analysis, using a recent technique called
the Cluster Treatment of Characteristic Roots (CTCR) for the first time on this class of time-delayed
systems. The CTCR paradigm is pursued after a block-diagonalization (mode-decoupling) transformation
on the system. This treatment produces some unique stability tables for the dynamics in the space
of the delays which are non-conservative and exhaustive. Second, a novel concept of spectral delay
space is presented, as an overture to the CTCR for the determination of the complete set of stabilitycrossing (switching) hypersurfaces in the delay space. Examples are provided to display the strengths
and efficiency of this new stability analysis mechanism.