Global asymptotic stability and projective lag synchronization for uncertain inertial competitive neural networks

Abstract

In this paper, the global asymptotic stability and projective lag synchronization of second‐order competitive neural networks with mixed time‐varying delays and uncertainties are studied without converting the original system into the usual first‐order system. Firstly, according to the Lyapunov functional method, inequality technique and the designed adaptive control strategy, the algebraic criteria of stability, and projective lag synchronization are derived by adjusting the control gain parameters in the controller. The obtained sufficient conditions are simple and easy to verify. Different from the traditional feedback controller, the adaptive controller can adjust its characteristics according to the system model, and external disturbance makes the system have better control performance. Besides, unlike the existing ones, this stability and synchronization problem is directly analyzed by constructing some new Lyapunov functionals with state variables and state variable derivatives. Finally, the effectiveness and practicability of the results are verified by numerical examples.