Abstract
The main contribution of this paper is a generalization of the Box Theorem, which was originally introduced for the Hurwitz case, for determining the robust Schur-stability of linear time-invariant discrete-time control systems containing an interval plant. This generalization provides necessary and sufficient conditions for the stability of a family of closed-loop characteristic polynomials <(z) = Q1,(z)P1(z) +... + Qm(z)Pm(z), where the Qis are fixed (controller) and then Pis are interval (plant) polynomials whose coefficients vary within a prescribed interval. This method requires checking a set of prescribed segment polynomials whose number is considerably less than that of the edges required by the edge theorem. A summary of the robust Schur-stability of discrete-time interval polynomials is presented.
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