**5. Conclusion**

This chapter presents a survey on the methods for numerical computation the maximal solution of a wide class of coupled Riccati-type equations arising in the optimal control of discrete-time stochastic systems corrupted with state-dependent noise and with Markovian jumping. In addition, computational procedures to compute this solution for a set of discrete-time generalized Riccati equations (7)-(8) are derived. Moreover, the LMI solvers for this case are implemented and numerical simulations are executed. The results are compared and the usefulness of the proposed solvers are commented.
