Feedback stabilization of discrete-time systems via the generalized Hermite-Biehler theorem

Considers the problem of characterizing all the constant gains that stabilize a given linear time-invariant discrete-time plant. First, two generalized versions of the discrete-time Hermite-Biehler theorem are derived and shown to be useful in providing a solution to this problem. A complete analytical characterization of all stabilizing feedback gains is provided as a closed form solution under the condition that the plant has no zeros on the unit circle. Unlike classical techniques such as the Jury criterion, Nyquist criterion, or root locus, the result presented here provides an analytical solution to the constant gain stabilization problem, which has computational advantages.