A Linear Fractional Transform (LFT) Based Model for Interconnect Uncertainty

Omar HAFIZ  Alexander MITEV  Janet Meiling WANG  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E92-A   No.4   pp.1148-1160
Publication Date: 2009/04/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E92.A.1148
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: VLSI Design Technology and CAD
Keyword: 
uncertainty,  process variation,  variational model order reduction,  linear fractional transform (LFT),  balanced truncation realization (BTR),  linear matrix inequality (LMI),  

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Summary: 
As we scale toward nanometer technologies, the increase in interconnect parameter variations will bring significant performance variability. New design methodologies will emerge to facilitate construction of reliable systems from unreliable nanometer scale components. Such methodologies require new performance models which accurately capture the manufacturing realities. In this paper, we present a Linear Fractional Transform (LFT) based model for interconnect parametric uncertainty. The new model formulates the interconnect parametric uncertainty as a repeated scalar uncertainty structure. With the help of generalized Balanced Truncation Realization (BTR) and Linear Matrix Inequalities (LMI's), the porposed model reduces the order of the original interconnect network while preserves the stability. The LFT based new model even guarantees passivity if the BTR reduction is based on solutions to a pair of Linear Matrix Inequalities (LMI's) generated from Lur'e equations. In case of large number of uncertain parameters, the new model may be applied successively: the uncertain parameters are partitioned into groups, and with regard to each group, LFT based model is applied in turns.