Journal of Applied Mathematics and Stochastic Analysis
Volume 11 (1998), Issue 4, Pages 519-526
Stabilization of nonlinear systems by similarity transformations
“Ecology”, Shpalernaya St. 36, St. Petersburg, Russia
Received 1 March 1996; Revised 1 November 1997
Copyright © 1998 Irina E. Zuber. 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.
For a system , , , where the pair
is given, we obtain the feedback vector to stabilize the
corresponding closed loop system. For an arbitrarily chosen constant
vector , a sufficient condition of the existence and an explicit form of a
similarity transformation is established. The latter
transforms matrix into the Frobenius matrix, vector into , and
an unknown feedback vector into the first unit vector. The boundaries
of are determined by the boundaries of , . The stabilization of the transformed system is subject to the
choice of the constant vector .