New approach on designing stochastic sampled-data controller for exponential synchronization of chaotic Lur'e systems

This paper investigates the problem of designing stochastic sampled-data controller for exponential synchronization of chaotic Lur'e systems (CLSs) via a new approach. Specially, first, multiple stochastic sampling intervals with given probabilities are considered and satisfy Bernoulli distribution. Second, unlike other studies, a unified probability framework, which takes sampling interval and time-varying delay into account, is proposed for the first time to design the controller. Based on this unified probability framework, an augmented Lyapunov-Krasovskii functional (LKF) with some new terms is constructed, which can take full advantage of the available information on actual sampling pattern. Different from some existing LKFs needing to be positive definite on the whole sampling intervals, by the new inequality in Lemma 1, the LKF is positive definite only requiring to be positive definite at sampling times. Third, less conservative synchronization criterion is derived and the desired stochastic sampled-data controller is designed. Finally, numerical simulations of Chua's circuit and neural network are provided to show the effectiveness and advantages of the proposed results.