Control Of Global Stochastic Synchronization For Semi-markovian Discontinuous Neural Networks

Discontinuous neural networks have abundant dynamic behavior due to the discontinuity of neuron activations,such as global finite time stability and synchronization.In this paper,the stochastic semi-Markovian process is introduced into the discontinuous neural network.The global stochastic finite-time synchronization problem for discontinuous neural networks with semi-Markovian switching is studied.The main content including:1.For the stochastic nonlinear systems with semi-Makovian switching,by applying Lyapunov-Krasovskii functional approach,stochastic analysis theory and inequality analysis technique,the stochastic finite-time stability theorem is established,and the corresponding global stochastic settling time calculation formula is derived.Furthermore,by designing the novel state-feedback controllers,which include discontinuous and integral terms,the conditions of global stochastic finite-time synchronization for discontinuous semi-Markovian switching neural networks under Brown noise disturbance are addressed.And the expressions about the upper bound of global stochastic settling time is given.2.Based on the event-triggered,by constructing appropriate Lyapunov-Krasovskii functionals with multiple integrals,applying differential inclusion theory,non-smooth analysis theory,general free-weighting matrix and Wirtinger-based multiple integral inequality approach,the H_? anti-synchronization is investigated under non-fragile controller for discontinuous neural networks with mixed time-varying delays and external disturbance,and the H_? anti-synchronization conditions are established in terms of linear matrix inequalities.3.A novel hybrid controller consisting of event-triggered controller,non-fragile controller and switching state feedback controller is designed.Under the stochastic distur-bance,the global stochastic finite-time synchronization for discontinuous neural network with mixed time-varying delays and semi-Markovian switching is discussed,the conditions are obtained.And the upper bound of the global stochastic setting time is evaluated accu-rately.