Input-to-state Stability on Formation Graphs

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. Comments Copyright 2002 IEEE. Reprinted from Proceedings of the 41st IEEE Conference on Decision and Control 2002, Volume 3, pages 2439-2444. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of the University of Pennsylvania's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it. This conference paper is available at ScholarlyCommons: http://repository.upenn.edu/ese_papers/117