Stable reduced models for nonlinear descriptor systems through piecewise-linear approximation and projection

Authors:
Bradley N. Bond;Luca Daniel
Affiliations:
Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA;Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA
Venue:
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Year:
2009

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Abstract

This paper presents theoretical and practical results concerning the stability of piecewise-linear (PWL) reduced models for the purposes of analog macromodeling. Results include proofs of input-output (I/O) stability for PWL approximations to certain classes of nonlinear descriptor systems, along with projection techniques that are guaranteed to preserve I/O stability in reduced-order PWL models. We also derive a new PWL formulation and introduce a new nonlinear projection, allowing us to extend our stability results to a broader class of nonlinear systems described by models containing nonlinear descriptor functions. Lastly, we present algorithms to compute efficiently the required stabilizing nonlinear left-projection matrix operators.