A Geometric Approach to Parameter Dependent Lyapunov Functions

Abstract

In this paper we investigate parameter dependent Lyapunov functions for the linear systems with a uncertain constant real parameter in terms of geometry. 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.