We present the solution to the algebraic Riccati-type equation of the state noise dependent linear-quadratic optimal control problem in terms of algebraic Lyapunov iterations. By properly initializing the sequence of algebraic Lyapunov iterations we obtained monotonic convergence from above to the positive definite stabilizing solution of the algebraic Riccati-type equation (the solution that represents the optimal solution to the corresponding optimal control problem). It has been shown that the proposed algorithm requires much less computational efforts than those previously used to solve the same problem.
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