  This paper investigates state feedback control laws for Markov jump linear
systems with state and mode-observation delays. An assumption in this study is
that the delay of mode observation obeys an exponential distribution. Also, we
raise an unknown time-varying state delay applied in the composition of the
state feedback controller. A method of remodeling the closed-loop system as a
standard Markov jump linear system with state delay is shown. Furthermore, on
the basis of this remodeling, several Linear Matrix Inequalities (LMI) for
designing feedback gains for stabilization and mixed $H_2/H_{\infty}$ control
are proposed. Finally, we apply a numerical simulation for examining the
effectiveness of the proposed mixed $H_2/H_{\infty}$ controller designing
method.
