Divergence Method for Exponential Stability Study of Autonomous Dynamical Systems

The recent proposed divergence method is used for investigation of an exponential stability of autonomous dynamical systems. New necessary conditions are derived by using Divergence theorem. Taking into account the relation between gradient and divergence of the vector field, novel sufficient conditions are obtained. These sufficient conditions are applied for design the state-feedback control laws ensuring exponential stability of the closed-loop system. Examples illustrate the efficiency of the proposed methods.