Contents 1 Introduction
In recent years, the control of the mean and variance values of the stochastic systems output are mainly discussed. We widely assumed that the system can be subjected to the Gaussian input noise in the traditional approach. But this is not always the case in the practical industry application. Recently, another approach has been developed to apply to the variables of arbitrary bounded stochastic distributions. This new strategy is based on the control of the output probability density function(PDFs). The PDFs has been stated by Wang [1] to represent either Gaussian or non-Gaussian bounded dynamical stochastic systems. For many practical systems such as, the particle size distribution control and combustion flames distribution control, the system representation has to be made between the input and output taken as the measured PDFs of the system rather than the input-output description. These types of stochastic systems are much more general in their forms than the classical ones. The PDFs are expressed by a linear combination of the B-spline basis functions through a set of coefficients. Once these basis functions are fixed, the dynamics of the stochastic system is then represented by a set of differential equations which dynamically link the coefficients of the B-spline expansions to the control input. Many results have been made in the theory and its applications [2] [13][14] [15], but the results are relatively few in the singular systems. Therefore, we will investigate the PDFs of the output for the stochastic singular system.
