On stabilizing gains far digital control systems

Abstract

In this paper, the authors develop an analytical criterion for determining the stabilizing gains of a digital control system. The criterion is based on analysis of the behaviour of a real polynomial X(u) constructed from the plant transfer function G(z). It is shown that the real zeros u/sub i/ of X(u)/spl isin/(-1, +1) and the signs of X/spl dot/(u)|/sub u=ui/ determine the range of stabilizing gains K completely, and in closed form. Besides providing a nongraphical and computationally simpler alternative to the Nyquist criterion and root locus techniques, this solution is a first step towards investigating stabilizability by higher order controllers.