Abstract: In this paper, the separative matrices of shifted Chebyshev series are introduced, which have an elegant recursive formla and a nice structure. By applying the property of the separative matrices, a new method for the identification of impulse response of linear systems via shifted Chebyshev series is presented. A direct approach to the output optimal control for systems characterized by impulse response function is also showed. Examples are included to demonstrate the validity and applicability of the approaches. Two methods are all suitable for MIMO systems.