On the Robustness of Mismatched Uncertain Dynamical Systems

Abstract

We consider the robustness problem of uncertain dynamical systems which do not satisfy the so-called matching conditions. We employ the controls which assure practical stability of the associated matched dynamical system. After introducing the idea of measure of mismatch, various conditions are stated, whose satisfaction assures that the mismatched uncertain system is practically stable under such a control. We also show that, under certain conditions, uniform attractivity can be assured; this has the advantage of reducing the measure of mismatch, and hence places lesser restrictions on the allowable magnitude of the uncertainty.