Stochastic finite-time synchronization for discontinuous semi-Markovian switching neural networks with time delays and noise disturbance

This paper deals with the global stochastic finite-time synchronization in probability for discontinuous semi-Markovian switching neural networks with time delays and noise disturbance. Firstly, the formula for calculating the global stochastic settling time of semi-Markovian switching nonlinear system with Brown motion is developed. Secondly, the novel state-feedback controllers, which include discontinuous factors and integral terms, are designed to realize the global stochastic finite-time synchronization goal. Under Filippov stochastic differential inclusion framework, by applying Lyapunov-Krasovskii functional approach, stochastic analysis theory, inequality analysis technique and the developed stochastic finite-time stability theorem, the global stochastic finite-time synchronization conditions are addressed in terms of linear matrix inequalities (LMIs). Moreover, the expressions about the upper bound of stochastic settling time are explicitly proposed. In addition, the relativity among the obtained results is analytically interpreted. Finally, two numerical examples are provided to demonstrate the validity of the proposed design methods and theoretical results.