Design-performance-measure statistics for stochastic linear control systems

Formulas for statistics of the standard integral quadratic performance measure used in stochastic linear control system design are derived. The formulas are expressed in terms of dynamical variables under the usual assumptions on noise, plant, and admissibility of control. All of these dynamical variables are expressed as linear transformations of plant state estimates. The practicality of this work, which is directed toward the establishment of new, statistically based design procedures for stochastic linear systems, is demonstrated by example.