Divergent stability conditions of dynamic systems

A new method for analyzing the stability of dynamic systems using the properties of the flow and divergence of the phase vector is proposed. A relation between Lyapunov's function method and this method is established. Based on the results obtained below, a design procedure of state feedback control laws for stabilizing dynamic systems is developed. The control law design is reduced to solving a differential inequality with respect to the control function desired. Examples illustrating the applicability of the new and existing methods are considered.