Bifurcations caused by non-affinity of singularly perturbed control systems

The problem of stabilization for non affine in control systems with guaranteed transient performances is discussed. The fast dynamic output feedback controller with the highest output derivative in feedback loop is used, where the controller is proper and can be implemented without ideal differentiation. Two-time-scale motions are induced in the closed-loop system and the method of singular perturbations is used to analyze the closed-loop system properties. Stability conditions imposed on the fast and slow modes and sufficiently large mode separation rate can ensure the output stabilization at the origin of non affine system in such a way that the transient performances are desired and insensitive to external disturbances and variations of nonlinear system parameters. The effect of fast-motion subsystem bifurcations caused by non-affinity of the control system is emphasized and numerical examples with simulation results are presented.