Variable gain intermittent stabilization and synchronization for delayed chaotic Lur'e systems

In this paper, a variable gain intermittent control strategy for stabilization and synchronization of chaotic Lur'e systems with time-varying delay is proposed. In contrast to the conventional constant gain intermittent control strategies, the proposed intermittent control strategy allows the control gain to vary with the operation duration of the intermittent controller. The construction of variable control gains is based on a partition scheme on the time-varying working intervals. In order to align with the structure of the variable intermittent control gain function, a pair of partition-dependent piecewise Lyapunov functions are introduced. Two distinct Razumikhin-type analysis techniques, one for the working intervals and the other for the resting intervals, are employed to derive novel criteria for intermittent stabilization and synchronization. The desired intermittent control/synchronization gain functions can be obtained by solving a convex minimization problem, which is capable of minimizing the control width under specified constraints on the gain norm. The numerical results demonstrate that, in comparison with the conventional constant gain strategies, the proposed variable gain intermittent control strategy is capable of efficiently reducing the intermittent control rate.