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Stable Reduced Models for Nonlinear Descriptor Systems Through Piecewise-Linear Approximation and Projection

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2 Author(s)
Bradley N. Bond ; Dept. of Electr. Eng. & Comput. Sci., Massachusetts Inst. of Technol., Cambridge, MA, USA ; Luca Daniel

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.

Published in:

IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems  (Volume:28 ,  Issue: 10 )