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. MAT-LAB code implementing the proposed algorithm is available from ftp: //next242.ece.orst.edu/pub/delsig.tar.Z.
An invariant set, S, is a set of points in state space having the pro erty that all trajectories emanating from points in S remain in Such sets are useful in the context of delta-sigma modulators since an invariant set yields rigorous theoretical bounds on the state variables and so establishes the stability of the modulator. This paper extends previously reported work for the second-order modulator aith a constant input to higher-order modulators and time-varying inputs. An invariant set for a 3"-order delta-sigma modulator is gwen which definitively proves that this modulator is stable.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.