Hybrid control of stochastic chaotic system based on memristive Lorenz system with discrete and distributed time-varying delays

This study investigates the problem of hybrid control of stochastic chaotic system based on memristive Lorenz system with discrete and distributed time-varying delays. First of all, the stochastic switched chaotic system is proposed based on Lorenz system modelled by piecewise linear memristor. Then, a novel hybrid controller is designed and the criteria are established to guarantee that the trivial solution of the corresponding stochastic system is exponentially stable in mean square. Furthermore, a novel technique is proposed to handle the problem of the difference, which cannot be depicted directly by stochastic Newton-Leibniz formula, between two state values of different instants between which there may exist impulse instants. Finally, an example is given to illustrate the efficiency and feasibility of the presented method.