ABSTRACT
A linear system with white noise added to the input and, often but not always, white noise added to the output is the most common model for randomness in control systems. It is the basis for Kalman filtering and the linear quadratic Gaussian (LQG) or H2 optimal regulator. This chapter presents the basic facts about linear systems andwhite noise and the intuition and ideas underlying them. Results are emphasized, not mathematically rigorous proofs. It is assumed that the reader is familiar with the elementary aspects of probability at, for example, the level of Leon-Garcia [1].
