Computational geometry is used to locate convex positively invariant sets for delta-sigma modulators. The existence of a positively invariant set implies the stability of the modulator and yields rigorous state bounds. Convex positively invariant sets for single-bit modulators up to order four, with a restricted class of time-varying inputs, have been found. MATLAB code implementing the proposed algorithm is available from ftp: //next242.ece.orst.edu/pub/delsig.tar.Z.
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Schreier et al. (1997) studied this question.
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