摘要: This paper deals with a general class of optimization problems in robust control with given expectation value of performance index, which can be transformed into the problem of matrix approximation with matrix inequalities constraints. Theorem for existence and the uniqueness of the solutions of matrix approximation with linear matrix inequalities (LMIs) constraints is presented and algorithms for solving the problems of matrix approximation with matrix inequalities constraints are given based on the fact that such problems can be converted into the generalized eigenvalue problem (GEVP) of LMI. Examples are given to illustrate the main results of the paper.