Contraction based stabilization of approximate feedback linearizable systems

A contraction based stabilization problem of systems with approximate strict feedback form is considered here. A high gain feedback is used to force the system into singularly perturbed form. Contraction theory based recursive controller design and singular perturbation analysis is used to design a stabilizing controller for the whole system. It is shown that, explicit error bounds between trajectories of fast subsystem and the slow manifold remain within the desirable limits by proper choice of controller parameters. Contraction theory based controller design and analysis has been expanded to a new class of systems.