Stochastic regularization and stabilization of hybrid functional differential equations

This work much extends our recent results published in SIAM Journal on Control and Optimization [1]. In lieu of switching jump diffusions, we examine stochastic systems with delays. We focus on stochastic regularization and stabilization for hybrid functional differential equations (FDEs). The main difficulty is that the hybrid functional systems without the linear growth condition grow much faster than linear and may have a finite explosion time. By introducing appropriate feedback controls (functions of Brownian motions), the perturbed hybrid functional systems become regular, and stable.