The problem of designing an observer for generating suboptimal controls for a linear discrete-time regulator when some of the plant state variables are not accessible is considered. The procedure is based essentially on a minimization of the resulting increase in cost. The dependence of this performance measure onw(0), the un-measurable part of the initial plant state vector, is eliminated by averaging the performance obtained for a linearly independent set of values forw(0). The design of the optimal observer is then carried out by minimizing this average value. This procedure is also shown to ensure the stability of the overall system