A study of linear time-varying systems subject to stochastic disturbances

Abstract

This paper is concerned with the analysis, in a stochastic sense, of systems described by linear differential equations with random disturbances, which often arise in the study of the variational behavior of an optimal control system along its nominal trajectory due to random disturbances in plant parameters or measuring errors in state variables.The random vector may be a white noise vector or may be generated by differential equations excited by white noise. By means of the Fokker-Planck equation the general result not only reveals the stability property of the system but also enables one to determine the state of the system at every instant of time in a stochastic sense. Experimental verification is given by simulating a second order system on an analog computer and the result is found to be in agreement with theory.