STABILIZATION ON ZERO-ERROR MANIFOLDS AND THE NONLINEAR SERVOMECHANISM PROBLEM

The extended-linearization methodology is applied to the nonlinear servomechanism problem for the case of time-varying exogenous signals. This yields a new approach to establishing exponential stability properties of trajectories that evolve on a certain invariant manifold which we call 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 exogenous signals can be treated. Also, a transmission zero condition for existence of the requisite zero-error manifold is given.