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

Anil Bose, Alan Cover, and James Reneke

 Deprtment of Mathemtical Science, Clemson University, Clemson 29634-1907, SC, USA
Received 27 January 1993; Revised 27 January 1997

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.