화학공학소재연구정보센터
IEEE Transactions on Automatic Control, Vol.46, No.7, 1080-1083, 2001
A modal decomposition of the Hopf normal form coefficient
The local stability of a nonlinear dynamical system at an equilibrium point with a pair of purely imaginary eigenvalues can be assessed through the computation of a cubic Hopf normal form coefficient, assuming the remaining eigenvalues have negative real parts, In this paper, a modal decomposition of the Hopf coefficient is proved. The decomposition provides a new methodology for analyzing the Hopf cubic normal form coefficient in a formal way, The framework is illustrated by nonlinear stability analysis of two control designs where it is shown that the Hopf coefficient can be stabilized through modal nonlinear feedbacks.