Sophisticating a naive Liapunov function for the prompt-jump model of a nuclear fission reactor at power

One source of positive definite Liapunov or V-functions for the direct determination of system stability is from an approximation to the dynamic equations that then admits the determination of a limit cycle of the approximated model. Such a function used in the true model may be unsatisfactory in failing to have a negative definite derivative function (dV/dt) at certain isolated points where (dV/dt) vanishes.. This paper shows how such naive Liapunov functions may be perturbed to rigorous functions by reference to the well-known second-order oscillation and then to the model of a power reactor in the prompt-jump approximation. The analysis produces a rigorous Liapunov function demonstrating stability in the large, sophisticating the naive function. (author)