Stabilization of stochastic functional differential systems by steepest descent feedback controls

The mean-square exponential stabilization and stochastically asymptotical stabilization for a class of stochastic functional differential systems is studied. Based on the definitions of derivatives of functionals, the generalized Ito operator for functionals and compound functions is established. Furthermore, the novel Lyapunov functionals and the induced steepest descent feedback controls are constructed to obtain such stability conditions that are weaker than the classical ones. Together with the generalized Ito operator and the steepest descent feedback controls, mean-square exponential stabilization and stochastically asymptotical stabilization for stochastic functional differential systems are investigated, respectively. As applications, two examples are given to illustrate the derived results: one is a stochastic mass-spring-damper model and the other is a numerical example with simulation figures.

Automated summary

The study focuses on mean-square exponential stabilization and stochastically asymptotical stabilization for a class of stochastic functional differential systems. By establishing the generalized Ito operator for functionals and compound functions, novel Lyapunov functionals and induced steepest descent feedback controls were constructed to obtain stability conditions weaker than the classical ones. The results were illustrated through two examples, including a stochastic mass-spring-damper model and a numerical example with simulation figures.