Abstract
This paper studies the distributed synchronization control problem of a class of stochastic dynamical systems with time-varying delays and random noise via randomly occurring control. The activation of the distributed adaptive controller and the update of the control gain designed in this paper all happen randomly. Based on the Lyapunov stability theory, LaSalle invariance principle, combined with the use of the properties of the matrix Kronecker product, stochastic differential equation theory and other related tools, by constructing the appropriate Lyapunov functional, the criterion for the distributed synchronization of this type of stochastic complex networks in mean square is obtained.
Highlights
In the human society and the objective world in which human society lives, complex networks can be seen everywhere, and there are various complex networks developed and constructed by humans intentionally or unintentionally: interpersonal networks, road networks, railway networks, power networks, the Internet, and news dissemination networks; there are various non-human complex networks that exist in the objective world: ecological networks, biological neural networks, metabolic networks, animal and plant gene networks, and so on
This paper studies the distributed synchronization control problem of a class of stochastic dynamical systems with time-varying delays and random noise via randomly occurring control
The model has the following characteristics: we use two Bernoulli random variables to describe the occurrence of distributed adaptive control, and update it according to a certain probability, and study the synchronization stability of stochastic complex networks by considering randomly occurring control and updating law
Summary
In the human society and the objective world in which human society lives, complex networks can be seen everywhere, and there are various complex networks developed and constructed by humans intentionally or unintentionally: interpersonal networks, road networks, railway networks, power networks, the Internet, and news dissemination networks; there are various non-human complex networks that exist in the objective world: ecological networks, biological neural networks, metabolic networks, animal and plant gene networks, and so on. The reference [12] considers that the complex network is disturbed by random mutations, it proposes a method of randomly occurring control and studies the synchronization behavior of stochastic dynamical systems, but it does not take into account the influence of coupling delay and random disturbance term time-delay. The model has the following characteristics: we use two Bernoulli random variables to describe the occurrence of distributed adaptive control, and update it according to a certain probability, and study the synchronization stability of stochastic complex networks by considering randomly occurring control and updating law. The results of this paper will enrich the synchronization control theory of stochastic dynamical systems on complex networks to a certain extent, and have important theoretical and application value
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