Mathematical Problems in Engineering
Volume 6 (2000), Issue 2-3, Pages 99-124

New results in subspace-stabilization control theory

C. D. Johnson

Department of Electrical and Computer Engineering, University of Alabama in Huntsville, 35899, AL, USA

Received 14 December 1998; Revised 27 October 1999

Copyright © 2000 C. D. Johnson. 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.


Subspace-stabilization is a generalization of the classical idea of stabilizing motions of a dynamical system to an equilibrium state. The concept of subspace-stabilization and a theory for designing subspace-stabilizing control laws was introduced in a previously published paper. In the present paper, two new alternative methods for designing control laws that achieve subspace-stabilization are presented. These two alternative design methods are based on: (i) a novel application of existing Linear Quadratic Regulator optimal-control theory, and (ii) an algebraic method in which the control-law is expressed as a linear feedback of certain “canonical variables.” In some cases, these new design methods may be more effective than existing ones. The results are illustrated by worked examples.