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 novel approach to establishing exponential manifold, known as 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. A transmission zero condition for existence of the requisite zero-error manifold is given.>