ABSTRACT
In many real control systems the plant to be controlled is subjected to random disturbances. Such a situation is the effect of gusts and random winds on the flight of an aircraft or launched missile. This chapter examines the techniques for predicting the average properties of the randomly excited responses of such a system. In many control applications measurements of these random responses are often contaminated by additive random measurement noise created in the measuring or telemetry system. In this case, the state of the system must be inferred by statistical estimation techniques using known statistical information about the disturbances and measurement noise. To discuss average properties of these random sequences, the chapter reviews some concepts from the theory of probability. The chapter aims to develop expressions for calculation of the statistical properties of the states and those of the measured system outputs for both transient problems and statistically stationary problems.
