Study of boundedness of the response of a nuclear reactor using Volterra series

Barrett has recently suggested the use of the majorant of a Volterra series for the determination of the system-response bounds. This reduces a nonlinear differential equation to an ordinary algebraic equation, thus considerably facilitating the study of the convergence properties of a Volterra-series expansion. The author has applied this method to a practical problem to investigate the effect of temperature-feedback control on the growth of neutrons in a nuclear-power reactor. This paper determines a sufficient condition for the boundedness of the response of the nuclear reactor subjected to an arbitrary, constantly acting, bounded input. The nonzero initial conditions of the system have been taken into consideration, and their effects on the system response are clearly shown.