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IMA Journal of Mathematical Control and Information 2003 20(3):277-304; doi:10.1093/imamci/20.3.277
© 2003 by Institute of Mathematics and its Applications
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Some new results in differential algebraic control theory

X. Y. Lu1 and S. P. Banks2

1 PATH, ITS, U.C. Berkeley, 1357 S. 46th Street, Richmond CA 94804-4648, USA 2 Department of Automatic Control & System Engineering PO Box 600, University of Sheffield, Sheffield S1 4DU, UK

In the differential algebra framework, static state and dynamic state feedback linearization are considered. The relationship between dynamic feedback and flatness defined by Fliess is discussed. The existence of an equivalent proper differential I–O system of a given differential I–O system is discussed, which is closely related to the choice of a proper fictitious output in control design. The concept flatness and its relation with dynamic feedback linearizability, controllability, observability, invertibility and minimal realization are discussed. Finally, it is demonstrated that many fundamental control concepts and their interrelationships can be incorporated into an extended control diagram.

Keywords: feedback linearizability; flatness; proper differential I–O systems; control diagram.

Received 3 June 2001. Revised 5 October 2002.


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