Response of linear systems with optimum controllers which do not require measurement of all state variables may be very sensitive to plant parameter variaitons. Previous results show that if these designs contain free parameters, the effect of variations of plant parameters on the performance index can be reduced significantly. This paper proves and generalizes some results previously given. A controllability concept in sensitivity design is denned which allows the designer to find the parameters of the controller which reduces plant sensitivity. The necessary and sufficient conditions in terms of the nominal system are given. If these conditions are not satisfied, then the controller parameters cannot be determined to minimize any selected measure of system sensitivity. An algorithm is proposed to solve for optimal and insensitive system to plant parameter variations for all initial conditions. The algorithm is very powerful and efficient and is not limited to low-order systems. An example is included to illustrate the design procedure.