Analytic determination of stabilizing gains for digital control systems
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In this paper we develop an analytical criterion for determining the stabilizing gains of a digital control system. The criterion is based on analysis of the behavior of a real polynomial X(u) constructed from the plant transfer function G(z). It is shown that the range of stabilizing gain K can be completely determined by the real zeros uiof X(u) lie in [-1, +1] and the signs of appropriate derivatives of X(u) evaluated at u=ui. The analytical solution given here is computationally simpler than the Nyquist criterion and is a first step towards investigating stabilizability by higher order controllers.
