Lagrange Stability in Reactors with a Linear Feedback

Two criteria for the Lagrange stability in reactors with an arbitrary linear feedback have been derived. The feedback kernel is assumed to be G(t) = rδ(t) + K(t), where r is the power-reactivity coefficient, and K(t), which is assumed to be bounded and integrable in (0, ^∞), represents other feedback effects. The Laplace transform of K(t) is denoted by (s). It is found that “a) if r < 0 and r + (s) = 0 has no positive real roots, and b) if K(x)dx ≤ 0 for all t ≥ 0 in the case of r = 0, then all the solutions of the kinetic equations are bounded.”