Simplified Lyapunov Stability for Chaotic Systems

Abstract

In this paper, based on Lyapunov stability theory, sufficient conditions are established for the local stabilization of the equilibrium point of a class of chaotic nonlinear systems. The proposed conditions are expressed as explicit algebraic inequalities, making them easy to verify without computing the eigenvalues of the Jacobian matrix. The results support the design of control strategies for suppressing chaos and stabilizing system trajectories. Their effectiveness is demonstrated through several three-, four-, and five-dimensional chaotic systems, with numerical simulations confirming the theoretical results.