Title :
Normal forms and bifurcations of control systems
Author :
Chang, D.-E. ; Kang, W. ; Krener, A.J.
Author_Institution :
Control & Dynamical Syst., California Inst. of Technol., Pasadena, CA, USA
Abstract :
We present the quadratic and cubic normal forms of a nonlinear control system around an equilibrium point. These are the normal forms under change of state coordinates and invertible state feedback. The system need not be linearly controllable. A control bifurcation of a nonlinear system occurs when its linear approximation loses stabilizability. We study some important control bifurcations, the analogues of the classical fold, transcritical and Hopf bifurcations
Keywords :
bifurcation; nonlinear control systems; stability; state feedback; control bifurcation; cubic normal forms; invertible state feedback; linear approximation; quadratic normal forms; stabilizability; Asymptotic stability; Bifurcation; Control systems; Eigenvalues and eigenfunctions; Linear approximation; Mathematics; Nonlinear control systems; Nonlinear systems; State feedback; Structural engineering;
Conference_Titel :
Decision and Control, 2000. Proceedings of the 39th IEEE Conference on
Conference_Location :
Sydney, NSW
Print_ISBN :
0-7803-6638-7
DOI :
10.1109/CDC.2000.912090
