Modeling Interconnect Variability Using Efficient Parametric Model Order Reduction
Proceedings of the conference on Design, Automation and Test in Europe - Volume 2
ICCAD '05 Proceedings of the 2005 IEEE/ACM International conference on Computer-aided design
Parameterized model order reduction via a two-directional Arnoldi process
Proceedings of the 2007 IEEE/ACM international conference on Computer-aided design
Positive Trigonometric Polynomials and Signal Processing Applications
Positive Trigonometric Polynomials and Signal Processing Applications
Factorization of multivariate positive Laurent polynomials
Journal of Approximation Theory
A new approach to modeling multiport systems from fequency-domain data
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
A Quasi-Convex Optimization Approach to Parameterized Model Order Reduction
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
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A parametrized model in addition to the control and state-space variables depends on time-independent design parameters, which essentially define a family of models. The goal of parametrized model reduction is to approximate this family of models. In this paper, a reduction method for linear time-invariant (LTI) parametrized models is presented, which constitutes the development of a recently proposed reduction approach. Reduced order models are computed based on the finite number of frequency response samples of the full order model. This method uses a semidefinite relaxation, while enforcing stability on the reduced order model for all values of parameters of interest. As a main theoretical statement, the relaxation gap (the ratio between upper and lower bounds) is derived, which validates the relaxation. The proposed method is flexible in adding extra constraints (e.g., passivity can be enforced on reduced order models) and modifying the objective function (e.g., frequency weights can be added to the minimization criterion). The performance of the method is validated on a numerical example.