On the stability of uncertain linear descriptor systems

Lyapunov stability theory for conventional systems is extended in a natural way to a class of uncertain descriptor (singular) systems with or without control. It is shown that the resulting stability can be determined via the solution of a generalized algebraic Riccati matrix equation. We first investigate the response upper bound and stability for the perturbed open-loop system, and then construct two types of robust stabilizers for systems possessing the properties of impulse controllability or normalizability.