Operator-Type Stability Theorem for Retarded Stochastic Systems With Application

In this note, asymptotic stability of general retarded stochastic systems is investigated by virtue of the so called operator-type technique. The method for rewriting system models via functional difference operators is proposed, and the asymptotic stability theorem based on functional difference operators is established. The models and conditions considered are all in general forms, and the results obtained are suitable for neutral systems. As a theoretical application, the delayed feedback control of general time varying linear stochastic systems with distributed delay is investigated, two control strategies are designed and the corresponding stability criteria are established. The efficiency of the operator-type technique is illustrated by an example.