Stabilizing schemes for piecewise-linear reduced order models via projection and weighting functions

Authors:
Bradley N Bond;Luca Daniel
Affiliations:
Massachusetts Institute of Technology, Cambridge, MA;Massachusetts Institute of Technology, Cambridge, MA
Venue:
Proceedings of the 2007 IEEE/ACM international conference on Computer-aided design
Year:
2007

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Abstract

In this paper we present several results concerning the stabilization of piecewise-linear reduced order models. We include proofs of internal and external stability for models whose system matrices possess special structures. We then introduce a new projection scheme, and a new set of weighting functions which allow us to extend some of these results to piecewise-linear systems comprised of arbitrary matrices, at least one of which is Hurwitz. Included are an algorithm for creating switching piecewise-linear reduced models comprised of globally exponentially stable systems, and stable simulation results for a system which produces unstable results when using the standard TPWL method.