International Journal of Mathematics and Mathematical Sciences
Volume 21 (1998), Issue 3, Pages 507-518
doi:10.1155/S0161171298000726
Linear feedback control of nonlinear systems with a dominating conservative quadratic term
Deprtment of Mathemtical Science, Clemson University, Clemson 29634-1907, SC, USA
Received 27 January 1993; Revised 27 January 1997
Copyright © 1998 Anil Bose et al. 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.
Abstract
Conditions are investigated for systems of the form Mx′=N+Ax+f(x), where f is quadratic,
which lield a point dissipative system. Application of the conditions are made to the problem of
existence of linear feedback controls u=Kx for systems of the form
Mx′=N+Ax+f(x)+Bu
which force the system to be point dissipative. The basic results have eztensions to more general
classes of systems.