3 Stationary Processes

Abstract

Much of the fundamental work done in the area of reduced order dynamic system optimization [1, 2] has been done in a setting which allows for a solution involving only algebraic equations rather than differential equations. This setting is in terms of time invariant linear systems driven by white noise processes. The basic assumption is that the processes considered are in steady state in a statistical sense, with a bounded constant second moment matrix. Technically, we refer to such systems as stationary stochastic processes [3]. The processes are dynamic in the sense that their states are moving with time. However, the statistics are constant.