Stabilizing Control Functions

A method for determining stabilizing control functions for any first-order controllable system is presented. Examples of stabilizing feedback control are examined and corroborated for stability using the second method of Liapunov. Consideration of a general class of arbitrary degree stabilizing feedback-control functions reveals that linear feedback control produces the greatest damping. Examination of signal error and time delay in the control function shows that highly damping control can result in system oscillation. Finally the method is extended to systems of higher order and a stabilizing control function is found for the reactor-kinetic equations even with unmonitored delayed neutrons if the linear feedback-control gain is > β/l.