This paper investigates the linear quadratic regulator(LQR) problem of
linear stochastic systems with Markovian jump. Firstly, two iterative
algorithms are proposed for solving the corresponding coupled algebraic
Riccati equa- tions (CAREs) based on the general-type Lyapunov equation
derived from linear stochastic systems. It is verified that the second
algorithm adding an adjustable factor converges faster than the first
one without it. Secondly, a monotonic convergence theorem is established
for the proposed iterative algorithms under certain initial conditions.
In the end, a numerical example is given to verify the efficiency of the
proposed algorithms.