In this paper, we present an observer-based controller design method which achieves performance robustness together with robust stability for linear multivariable systems with structured uncertainties. The performance robustness means that the deterioration of control performance is suppressed when we compare the transient behaviour for the uncertain system with a desired one generated by using the nominal system directly and at the same time excessive control input is avoided. In this approach, we adopt a similar way to the model-following technique and assume that the control law consists of a state feedback law for the nominal system and a compensation input for the purpose of preventing the error between the transient behaviour for the uncertain system and the desired one. The compensation input is additional modification term given by feedback form of an estimated error signal and is determined so that an upper bound of a quadratic cost function for the error system between the real trajectory for the plant and the desired one is minimized. We show that a condition for the existence of the compensation input which minimizes an upper bound of the quadratic cost function for the error system is given in terms of linear matrix inequalities (LMIs). Finally, numerical examples are presented.