This paper presents a numerical algorithm for solving non-linear algebraic equations generated in an optimization problem in which the sum of a quadratic performance criterion and the H2-norm of the closed-loop transfer function from a Gaussian white noise stochastic disturbance to the state space variables of a linear time invariant system is minimized. The proposed algorithm is given in terms of algebraic Lyapunov equations. It is shown in this paper that this algorithm converges to the local minimum under non-restrictive, control theory and applications-oriented assumptions, stabilizability and detectability.
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