Projective Synchronization of Uncertain Linear Systems With Stochastic Perturbations via Discontinuous Adaptive Odd Impulsive Control

This article studies the discontinuous adaptive odd impulsive control for the projective synchronization of uncertain linear systems with stochastic perturbations. Although the traditional discontinuous adaptive impulsive control can realize system stability, the adaptive law needs to be updated for all impulsive instants, which leads to high design complexity and consumes considerable computational resources. To this end, this article proposes an odd impulsive strategy. Under the strategy, the adaptive law is focused on the odd impulsive instants, and the even impulses only need to be located between two adjacent odd impulses without additional constraints. This approach significantly reduces the computational cost of controller design and implementation, which enhances system flexibility, and simplifies the verification of convergence conditions. In addition, this article proves the correctness of the proposed adaptive law for uncertain linear systems, and provides a numerical example to verify the effectiveness of our results.