On Lyapunov stability of a family of nonlinear time-varying systems

Investigates several types of Lyapunov stability of an equilibrium of a family of finite dimensional dynamical systems determined by ordinary differential (difference) equations. By utilising the extreme systems of the family of systems, the authors establish sufficient conditions, as well as necessary conditions (converse theorems) for several robust stability types. The authors´ results enable them to realize a significant reduction in the computational complexity of the algorithm of Brayton and Tong in the construction of computer generated Lyapunov functions. Furthermore, the authors demonstrate the applicability of the present results by analyzing robust stability properties of equilibria for Hopfield neural networks and by analyzing the Hurwitz and Schur stability of interval matrices