Abstract
Stochastic feedback control has aroused folks’ notice, but little is known on the roles of stochastic noises for the dynamic behavior of impulsive differential systems. In this paper, we mainly study the problem of stochastic stabilization on explosive solutions of nonlinear impulsive differential systems by noises. Under the one-sided polynomial growth condition, a nonlinear impulsive differential system may explode at a finite time. To suppress the explosive solution, we introduce two independent stochastic noises (polynomial and linear) such that there exists a unique global solution for the corresponding stochastically perturbed impulsive differential system, and the global solution is bounded and almost surely exponentially stable.
Highlights
Deterministic differential systems (DSs) are usually used to describe real problems
Growing researchers began to study the roles played by stochastic noises on the dynamic behavior of the solutions of deterministic DSs (e.g. [5]–[12])
Motivated by the thought of stochastic stabilization, the following question is proposed spontaneously: if the solution of an impulsive differential system explodes at a finite time on an impulsive interval, can we add some stochastic noises such that the stochastically perturbed impulsive differential system has a unique global solution and the unique global solution decays to zero solution? This will fill in the blank and is our main contribution
Summary
One of the most desired issues in the investigations and applications of deterministic DSs is the character of asymptotic stability. Deterministic DSs, whose coefficients are polynomials or controlled by polynomials, are an important class of nonlinear systems, such as LotkaVolterra (L-V) systems. Mao and his coauthors [13]–[15] showed that stochastic noises can suppress the explosive. [34], [35]), but, as far as we know, there is little literature on the roles of stochastic noises on the dynamic behavior of impulsive differential systems. Our aim is to investigate the roles of stochastic noises for impulsive differential systems. Motivated by the thought of stochastic stabilization, the following question is proposed spontaneously: if the solution of an impulsive differential system explodes at a finite time on an impulsive interval, can we add some stochastic noises such that the stochastically perturbed impulsive differential system has a unique global solution and the unique global solution decays to zero solution? This will fill in the blank and is our main contribution
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
