Output tracking control of a class of nonlinear non-minimumphase or critically minimumphase systems via backstepping procedure

Output tracking control of non-minimumphase or critically minimumphase systems is a highly challenging problem encountered in the control of flexible manipulators, space structures and elsewhere. In this paper, a class of nonlinear multi input-multi output non-minimumphase or critically minimumphase cascade systems have been considered. By defining the tracking error, the tracking problem is reduced to a regulation problem and a time-varying system is obtained. It is shown that this time-varying system can be divided into two parts, a time-invariant part and a time-varying part. With the smooth stabilizability assumption of the time-invariant part, the discontinuous control law, u₁, is obtained via the backstepping procedure. It is shown that in the discontinuous points of u₁, the internal dynamics are input-to-state stable, so they are bounded. Therefore, they can be ignored in the design of control law u₂. Finally, it is illustrated that this discontinuous time-varying feedback law, u, includes u₁ and u₂ guarantees the asymptotic stability of the tracking error and the boundedness of the zero dynamics.