On the discrete JLQ and JLQG problems

In this paper the optimal control law for the discrete infinite time-varying stochastic control system with jumps and quadratic cost is found under the assumption that the coefficients have limits as time tends to infinity and the boundary system is absolutely observable and stabilizable. Such assumptions allow to construct the optimal control in the time invariant feedback form. To solve the arising JLQG problem asymptotic properties of the solution of the difference Riccati equations for discrete time markoviari jump linear quadratic control problem with time varying coefficient are established.