Robustness of nonlinear control systems with respect to unmodeled dynamics

We examine the global stability properties of nonlinear controllers in the presence of high frequency unmodeled dynamics. We develop necessary and sufficient conditions for a general class of nonlinear control laws, under which global signal boundedess or asymptotic stability is guaranteed. We show that a wide class of nonlinear control laws does not satisfy these conditions and therefore does not guarantee global stability in the presence of high frequency unmodeled dynamics.