title: Impulsive control of stochastic systems with applications in chaos control, chaos synchronization, and neural networks.
abstract: Real systems are often subject to both noise perturbations and impulsive effects. In this paper, we study the stability and stabilization of systems with both noise perturbations and impulsive effects. In other words, we generalize the impulsive control theory from the deterministic case to the stochastic case. The method is based on extending the comparison method to the stochastic case. The method presented in this paper is general and easy to apply. Theoretical results on both stability in the pth mean and stability with disturbance attenuation are derived. To show the effectiveness of the basic theory, we apply it to the impulsive control and synchronization of chaotic systems with noise perturbations, and to the stability of impulsive stochastic neural networks. Several numerical examples are also presented to verify the theoretical results.
authors.affiliation: Centre for Nonlinear and Complex Systems, School of Electronic Engineering, University of Electronic Science and Technology of China, Chengdu 610054, People's Republic of China.
authors.forename: Chunguang
authors.initials: C
authors.lastname: Li
authors.forename: Luonan
authors.initials: L
authors.lastname: Chen
authors.forename: Kazuyuki
authors.initials: K
authors.lastname: Aihara
mesh_terms: D000465:Algorithms; D001703:Biophysics / Q000379:methods*; D003198:Computer Simulation; D005246:Feedback; D015233:Models, Statistical; D016571:Neural Networks, Computer; D017711:Nonlinear Dynamics; D010363:Pattern Recognition, Automated; D015203:Reproducibility of Results; D012984:Software; D013269:Stochastic Processes; D013598:Systems Theory