Robustness of nonlinear control systems with respect to unmodeled dynamics

In theory, it can be established that nonlinear control laws for linear or nonlinear plants can be used to meet strict performance requirements. The success of these control designs in practical situations will very much depend on whether they can still meet the expected performance characteristics in the presence of inevitable modeling errors. In this paper, we develop necessary and sufficient conditions for a general class of nonlinear control laws in the presence of high-frequency unmodeled dynamics, under which global signal boundedness 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.