New criteria for stochastic suppression and stabilization of hybrid functional differential systems

Abstract

This paper establishes new criteria for stochastic suppression and stabilization of hybrid functional differential systems with general one-sided polynomial growth condition. For an unstable nonlinear hybrid functional differential system with general one-sided polynomial growth condition, two independent Brownian noise processes are used to perturb the system into the stochastic hybrid differential system. Theoretical analysis shows that one of the nonlinear diffusion terms may suppress the explosive solution of deterministic system, and the other one can make the perturbed hybrid system almost surely stable with general decay rate.