Abstract: In this paper, some problems for linear constant system with quadratic performance indices are discussed. It includes the composite optimal control problem for reduction of the performance index sensitivity, as well as trajectory sensitivity, and composite optimal control problem for placement of the closed-loop poles. The new composite performance indices are presented to obtain better results, and computations are readily performed. The expression of the gradient matrix of closed-loop eigenvalues with respect to the matrix Q is derived. An algorithm for the matrix Q is given for placement of the distinct all closed-loop poles, as well as a numericdl example are given.