Stability For Markovian Jumping Neural Network And Thechaotic Memristor-Based Chua’s Oscillator

Neural networks(NNs), which usually show stability, periodic oscillation or chaotic behavior, have been a subject of intense research activities due to their wide applications in different areas such as image processing, pattern recognition,associative memory and combinational optimization. In this paper, Based on differential inclusions, non-smooth analysis, Lyapunov method, and linear matrix inequality(LMI), by design appropriate controllers, this dissertation studies the exponential state estimation issue of Markovian jumping neural networks with mixed time-varying delays and discontinuous activation functions, adaptive anti-synchronization control issues of the chaotic memristor-based canonical Chua’s oscillatorsynchronization. The main content of the dissertation is listed as follows:(1)The exponential state estimation issue for Markovian jumping neural networks with mixed time-varying delays and discontinuous activation functions is investigated,where the nonlinear perturbation of the measurement equation is assumed to be locally Lipschitzian. By introducing triple-integral terms and quadruple integrals term in Lyapunov-Krasovskii functional, the obtained Lyapunov matrices are distinct for different system modes. Based on the nonsmooth analysis theory and by applying stochastic analysis techniques, the full-order state estimator is designed to ensure that the corresponding error system is exponentially stable in mean square. The desired mode-dependent and delay-dependent estimator can be achieved by solving a set of linear matrix inequalities(LMIs).(2)The adaptive anti-synchronization control issues for the chaotic memristor-based canonical Chua’s oscillator.Firstly, divided the error system into four different cases according to the i-v characteristics of memristive neural networks. Secondly, By means of Lyapunov-Krasovskii functional stability theory and approach, State the adaptive state-feedback controllers are designed respectively such that the response system can be anti-synchronization with corresponding drive system.