On stabilizing gains far digital control systems

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_i of X(u)∈(-1, +1) and the signs of X˙(u)|_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.