Stability criteria for linear control systems

Abstract

The stability criterion formulated by Nyquist¹ is sometimes difficult to apply. The method proved here is algebraic rather than geometric and, for a certain class of problems, leads to a simple technique readily usable in designing systems involving several parameters. The criteria discussed are embodied in three conditions.Thus it is possible to leave some design constants unspecified, and fix them in the best way to ensure stability. This implies a synthetic rather than an analytic approach to circuit design, a feature distinguishing the present method from others which rapidly become unmanageable when even a few design constants are carried.It is also shown how high-degree equations arising from the transfer function can be discussed using only the elementary theory of quadratics. The method is compared with the Routh-Hurwitz approach.