Exact and Exhaustive Stability Analysis of Linear Consensus Protocols with Time-Delay

Date of Completion

January 2012


Engineering, Mechanical




In the general area of multi-agent coordination and control, one of the most broadly studied topics is the consensus problem. The objective of a consensus protocol is to guarantee that the members of the swarm reach an agreement on a certain variable of interest by taking decisions based on a partial knowledge of the state of the whole group. This is normally required as a first step towards a more complex task, such as formation control, area coverage, or coordinated attack. The effect of time delays on this coordination problem is also broadly studied, considering that they are unavoidable in practical systems. Despite the huge amount of relevant literature to date, there is no apparent exact stability analysis methodology for consensus protocols with respect to the time delay (or multiple time delays). ^ The research process that led to this dissertation focused on the study of this particular problem. The main contribution is a structured methodology which can generate, very efficiently, an exact, exhaustive and explicit stability map of a linear consensus protocol with respect to the time delay(s). This methodology is based on the combination of a decoupling property, characteristic of multi-agent consensus systems, and the Cluster Treatment of Characteristic Roots, CTCR, paradigm. While the decoupling of the system simplifies the problem and reduces the computational load to increase efficiency, CTCR is the paradigm that enables the stability analysis in the domain of the time delay(s). ^ The new proposed methodology allows the study of systems with single and multiple time delays, and with undirected and directed communication topologies. The effect of the delay on the relative stability is also studied, and it is shown that, under certain conditions, an increase in the delay can improve the performance of the consensus system. As an important extension of the traditional consensus protocol, a formation control algorithm, also affected by time delays, is proposed and studied. ^