Guaranteed cost for stochastic systems with unknown transitions jump rates

This paper deals with the class of continuous-time stochastic systems with totally known and totally unknown, but bounded with some known bounds, transition jump rates. The guaranteed cost control problem of this class of systems is tackled. New sufficient conditions for guaranteed cost are developed. A design procedure for the guaranteed cost controller which guarantees that the closed-loop dynamics will be stable is proposed. It is shown that the addressed problems can be solved if the corresponding developed convex optimization problems are feasible. A numerical example is employed to show the usefulness of the proposed results.