Practical Stabilization of Systems with a Fold Control Bifurcation

Abstract

Nonlinear parameterized dynamical systems exhibit complicated performance around bifurcation points. As the parameter of a system is varied, changes may occur in the qualitative structure of its solutions around an equilibrium point. Usually, this happens when some eigenvalues of the linearized system cross the imaginary axis as the parameter changes [7]. For control systems, a change of some control properties may occur around an equilibrium point, when there is a lack of linear stabilizability at this point. This is called a control bifurcation [21]. A control bifurcation occurs also for unparameterized control systems. In this case, it is the control that plays the parameter’s role in parameterized dynamical systems.