Distributed control of vehicle formations: A decomposition approach

In this article we consider the problem of designing a controller for a formation of vehicles. We present a novel method that allows the synthesis of distributed controllers with H_¿ performance; the method is based on a modal decomposition technique and it makes use of LMIs (linear matrix inequalities). One of the interesting results of this paper is that for certain relevant situations the size of the synthesis LMIs is independent of the size of the formation: this means that with a single, small LMI test it is possible to compute a controller with guaranteed disturbance rejection performance for all the formations of a kind. This method can then be considered as a significant generalization of the famous result presented by Fax and Murray, where the authors showed a how it was possible to prove the stability of a formation with a single Nyquist diagram, irrespectively of the formation size.