Analysis and synthesis of control systems

On sufficient and necessary conditions of asymptotic stability of nonlinear dynamic systems

V. P. Zhukov

Institute of Control Sciences, Russian Academy of Sciences

Abstract: New sufficient and necessary conditions for asymptotic stability of equilibrium states of autonomous dynamic systems governed by Cauchy-type ordinary differential equations of any order are derived. The application of a special function class (instead of Lyapunov functions) allowed to prove the asymptotic stability converse with clear geometric meaning.

UDC: 62-501.52