Stabilization on zero-error manifolds and the nonlinear servomechanism problem

The extended-linearization methodology is applied to the problem of designing a control law for a nonlinear plant in order to achieve asymptotic tracking of classes of time-varying reference inputs with asymptotic rejection of classes of time-varying, unmeasured disturbances. This involves a novel approach to establishing exponential stability properties of trajectories that evolve on a certain invariant manifold called the zero-error manifold. Advantages of the approach are that the underlying theory is relatively simple, and that a requirement of small derivatives for the exogenous signals is used rather than a requirement that the exogenous signals remain small. Thus, certain cases of unbounded reference or disturbance signals can be treated. Finally, a transmission zero condition for the existence of the requisite zero-error manifold is given