International Journal of Stochastic Analysis

International Journal of Stochastic Analysis / 1998 / Article

Open Access

Volume 11 |Article ID 630894 | 8 pages | https://doi.org/10.1155/S1048953398000422

Stabilization of nonlinear systems by similarity transformations

Received01 Mar 1996
Revised01 Nov 1997

Abstract

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.

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