On an Analysis of the Response of Linear Systems Subjected to Partially Independent Random Inputs by Using Stochastic Matrices

Abstract

In the analysis of control systems, it is often required to know the statistical properties of the response of the systems to random input signals. Conventional methods depend upon the utilization of the convolution integrals and mean value and auto-correlation function of the input signals. The results gotten by these methods are time averages of whole responses. But when the statistical properties at specified time, for instance, at the time of changes of the input signal are required, these methods are not effective.
In this paper the method of stochastic matrix is introduced and a method of analysis for linear systems subjected to partially independent input signals is presented. This method is useful for the analysis of relay systems and other systems with partially independent inputs.
Firstly the general form of the method is presented and as an example the responses for semi-Markovian inputs are analysed theoretically and experimentally. The results verify the usefulness of this method.