Slow and fast stability in singular systems

Abstract

We consider the problem of robust feedback control of LTI systems in the presence of parasitics. An essential related concept is that of fast stability -- a type of stability characterizing parasitics or high-frequency effects. A rigorous definition of fast stability is formulated in terms of topologies on a certain differentiable manifold and is connected with the robust feedback problem. A generic solution is given along with illustrative examples.