Geometrical approach to parameter dependent Lyapunov functions

Abstract

In this paper we consider the problem of constructing parameter dependent Lyapnov functions that guarantee the stability of the linear systems with an uncertain constant real parameter. First we formulate the surface on which all parameter dependent Lyapunov matrices for a given uncertain system exist. Next, after defining a Riemannian metric on the surface, we derive a method to obtain a parameter dependent Lyapunov matrix as a geodesic on the surface.