On the Stabilization of Uncertain Linear Systems via Bound Invariant Lyapunov Functions

Abstract

This paper considers the problem of stabilizing a class of systems with an arbitrarily large uncertainty bounding set. In particular, the stabilization of linear uncertain systems via a bound-invariant Lyapunov function is examined. Necessary and sufficient conditions for the existence of a bound invariant Lyapunov function are derived for systems with block structured uncertainty and a class of systems with scalar linear uncertainty.