Robust control of a class of MIMO minimum-phase nonlinear systems

Studies robust control of a class of multi-input multi-output uncertain minimum-phase nonlinear systems :q which are input/output invertible but do not have well defined relative degree. It is known that this class of MIMO nonlinear systems cannot be transformed, via a change of coordinates and a state feedback, into a lower dimensional subsystem (which is the zero dynamics of the original system) driven by a set of chains of integrators, but more complicated interconnected structures. Sufficient conditions are presented for the existence of a nonlinear robust controller that achieves global asymptotic stability, uniformly on the unknown time-varying disturbances d(t) whose bound is known. The state feedback control law is explicitly constructed by using a Lyapunov-based recursive design procedure, i.e., the backstepping method. In the case when d(t) represents an unknown constant vector parameter and appears linearly in the nonlinear system, an adaptive controller is also developed, achieving global stability with state regulation