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Mathematical Problems in Engineering
Volume 2007, Article ID 54212, 17 pages
Research Article

On Bumps and Reduction of Switching Transients in Multicontroller Systems

1Centre de Recherche en Automatique de Nancy (CRAN), (UMR 7039), Faculté des Sciences et Techniques, Nancy-Université, BP 239, Boulevard des Aiguillettes, Vandoeuvre Cedex 54506, France
2Service d'Automatique et d'Analyse des Systèmes, Université Libre de Bruxelles, CP 165/55, Avenue F. D. Roosevelt 50, Brussels 1050, Belgium

Received 29 July 2006; Accepted 5 February 2007

Academic Editor: P. T. Kabamba

Copyright © 2007 Joseph J. Yamé and Michel Kinnaert. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper is concerned with the realization and implementation of multicontroller systems, consisting of several linear controllers, subject to the bump phenomenon which occurs when switching between one controller acting in closed loop and another controller in the set of “offline” controllers waiting to take over the control loop. Based on a deep characterization of the bump phenomenon, the paper gives a novel and simple parameterization of such set of linear controllers, possibly having different state dimensions, to cope with bumps and their undesirable transients in switched-mode systems. The proposed technique is based on a non minimal state-space representation allowing a common memory and a unique dynamics shared by all controllers in that set. It also makes each initially open-loop unstable controller run in a stable way regardless of whether that controller is connected to the controlled process.