The matrix equation AT P + PA = - Q is a useful equation for the study of the stability of a system when the dynamics are characterized by X = AX. The matrix or system is stable if and only if the solution matrix P is positive definite for a positive definite matrix Q. This paper describes a new computational method of finding P when A and Q are known. The method is simple and efficient with matrix operations of the same order as A.
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Beavers et al. (1975) studied this question.
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