Qualitative analysis of dynamical systems determined by differential inequalities with applications to robust stability

In this paper we develop a Lyapunov stability theory for finite dimensional continuous-time dynamical systems described by a system of first-order ordinary differential inequalities. We utilize this theory to establish sufficient robust stability criteria for a large class of finite dimensional, continuous-time dynamical systems described by systems of ordinary differential equations. We demonstrate the applicability of the methodology advanced herein by means of a specific example that has been considered in the literature. In terms of computational complexity and conservatism of stability criteria, the present results frequently offer improvements over existing results