Stable Reduced Models for Nonlinear Descriptor Systems Through Piecewise-Linear Approximation and Projection
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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.
Date issued
2009-09Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science; Massachusetts Institute of Technology. Research Laboratory of ElectronicsJournal
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Publisher
Institute of Electrical and Electronics Engineers
Citation
Bond, B.N., and L. Daniel. “Stable Reduced Models for Nonlinear Descriptor Systems Through Piecewise-Linear Approximation and Projection.” Computer-Aided Design of Integrated Circuits and Systems, IEEE Transactions on 28.10 (2009): 1467-1480. © 2009 IEEE
Version: Final published version
ISSN
0278-0070
Keywords
stability, nonlinear systems, model order reduction (MOR), Analog macromodeling