International Journal of Stochastic Analysis

International Journal of Stochastic Analysis / 1998 / Article

Open Access

Volume 11 |Article ID 630894 | 8 pages |

Stabilization of nonlinear systems by similarity transformations

Received01 Mar 1996
Revised01 Nov 1997


For a system x˙=A(x)+b(x)u, u(x)=s(x)x, xn, where the pair (A(x),b(x)) is given, we obtain the feedback vector s(x) to stabilize the corresponding closed loop system. For an arbitrarily chosen constant vector g, a sufficient condition of the existence and an explicit form of a similarity transformation T(A(x),b(x),g) is established. The latter transforms matrix A(x) into the Frobenius matrix, vector b(x) into g, and an unknown feedback vector s(x) into the first unit vector. The boundaries of A˜(y,g) are determined by the boundaries of {kA(x)xk,kb(x)xk}, k=0,n1¯. The stabilization of the transformed system is subject to the choice of the constant vector g.

Copyright © 1998 Hindawi Publishing Corporation. 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.

84 Views | 274 Downloads | 7 Citations
 PDF  Download Citation  Citation
 Order printed copiesOrder

We are committed to sharing findings related to COVID-19 as quickly and safely as possible. Any author submitting a COVID-19 paper should notify us at to ensure their research is fast-tracked and made available on a preprint server as soon as possible. We will be providing unlimited waivers of publication charges for accepted articles related to COVID-19. Sign up here as a reviewer to help fast-track new submissions.