On the discrete JLQ and JLQG problems

In this paper the optimal control law for the discrete infinite time-varyin g stochastic control system with jumps and quadratic cost is found under th e assumption that the coefficients have limits as time tends to infinity an d the boundary system is absolutely observable and stabilizable. Such assum ptions allow to construct the optimal control in the time invariant feedbac k form. To solve the arising JLQG problem asymptotic properties of the solu tion of the difference Riccati equations for discrete time markovian jump l inear quadratic control problem with time varying coefficient art, establis hed.