Departmental Papers (ESE)


Formation stability is now analyzed under a new prism using input-to-state stability. Formation ISS relates leader input to internal state of the formation and characterizes the way this input affects stability performance. Compared to other notions of stability for interconnected systems, formation ISS does not require attenuation of errors as they propagate, but instead quantifies the amplification and provides worst case bounds. The control interconnections that give rise to the formation are represented by a graph. The formation graphs considered are built from a small number of primitive graphs, the stability properties of which are used to reason about the composite. For the case of linear dynamics, a recursive expression allows the calculation of the bounds using the graph theoretic representation of the formation via the adjacency matrix. Illustrative examples demonstrate how formation ISS can be used as an analysis and a design tool.

Document Type

Conference Paper

Subject Area


Date of this Version

December 2002


Copyright 2002 IEEE. Reprinted from Proceedings of the 41st IEEE Conference on Decision and Control 2002, Volume 3, pages 2439-2444.

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Date Posted: 04 August 2005