Improved switching controllers for finite-time synchronization of delayed neural networks with discontinuous activations

This paper considers time-delayed and discontinuous neural networks described by a class of functional differential inclusions. Without assuming the boundedness and monotonicity of the discontinuous activation functions, the finite-time synchronization control of the drive-response neuron system is studied. First, we propose a set of novel switching state-feedback controllers and switching adaptive controllers. Second, we give some sufficient conditions to control the synchronization error to converge zero in a finite time. Moreover, these conditions are easily checkable. The dynamic analysis here employs the set-valued analysis, the extended Filippov-framework, the famous finite-time stability theorem and the generalized Lyapunov functional method. Finally, numerical examples and computer simulations are presented to confirm and demonstrate the theoretic findings.