Passivity-based robust feedback control for non-linear systems with input dynamical uncertainty

This paper addresses the robust feedback control problem for a class of non-linear systems with uncertain input dynamics. The main objective is to develop a passivity-based systematic design approach for this kind of uncertain system. First, a passivity condition is presented for a non-linear system in feedback interconnection form, and then it is shown that with the help of this condition, a state feedback control law can be designed to render the uncertain system passive. Moreover, the extensions of the passivation controller are investigated in two cases where the uncertainty allows unknown control direction and there exists the external disturbance, respectively. It will be shown that an adaptive controller with a Nussbaum-type function can be incorporated into the passivation controller to deal with the unknown control direction and the L ₂-gain performance can be achieved by gain re-assignment of the passivation controller. Finally, a numerical example is given to demonstrate the proposed approach.