Asymptotic Stability of Nonlinear Systems with Holomorphic Structure

Abstract

We consider the local asymptotic stability of a system dx/dt = F(z), z = C sup n , F : C sup n - C sup n is holomorphic, t  R, and show that if the system is locally asymptotically stable at some equilibrium point in the N sup th approximation for some N , then necessarily its linear part is asymptotically stable also.