Stabilisation of stochastic systems with optimal decay rate

The authors deal with the problem of exponential stabilisation for continuous-time stochastic systems. Several equivalent characterisations are presented for exponential stability of continuous-time stochastic systems. The relationship between decay rate and the spectral abscissa of an operator associated with a stochastic system is investigated. On the basis of this relationship, optimal controllers are designed for continuous-time stochastic systems. Finally, an example is provided to illustrate the method.