Bradley Bond:

Title:
"Stabilizing Schemes for Piecewise-Linear Reduced Order
Models via Projection and Weighting Functions."

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.