A Simple Stability Criterion

Abstract

A quick method is described by which it may be determined for which ranges of gain, K, all the roots of the characteristic equation have negative real parts. These ranges of stability are determined by the relative position of two curves. The curves also indicate where the stability is marginal. The method is especially well suited for multiple loop systems as it is based on the coefficients of the powers of s. The criterion does not require any tables, charts, or special equipment. Few calculations are needed and they are all of the simplest nature with real numbers. Instead of gain K could be a damping ratio, time constant, and so forth.