Matrix-Interpolation-Based Parametric Model Order Reduction for Multiconductor Transmission Lines With Delays

Abstract

Abstract-A novel parametric model order reduction (PMOR) technique based on matrix interpolation for multicondutor transmission lines with delays having design parameter variations is proposed in this paper. Matrix interpolation overcomes the oversize problem caused by input-output system level interpolation based parametric macromodels. The reduced state-space matrices are obtained using a higher-order Krylov subspace based model order reduction technique which is more efficient in comparison to the Gramian based parametric modeling where the projection matrix is computed using a Cholesky factorization. The design space is divided into cells and then the Krylov subspaces computed for each cell is merged and then truncated using an adaptive truncation algorithm with respect to their singular values to obtain a compact common projection matrix. The resulting reduced order state-space matrices and the delays are interpolated using positive interpolation schemes making it computationally cheap and accurate for repeated system evaluations under different design parameter settings. The proposed technique is successfully applied to RLC and multiconductor transmission line circuits with delays.

Truncated Prediction Output Feedback Control of a Class of Lipschitz Nonlinear Systems With Input Delay

“…The presence of time delays, if not considered in the controller design, may seriously degrade the performance of the controlled system. For the analysis and control of circuit systems, time delay must be included during the process of modeling when the geometric dimensions become electrically large and the frequency content of signal waveform increases [1]. Indeed, the importance of addressing delay in the control design has been well recognized for a long time [2].…”

A Passivity-Preserving Frequency-Weighted Model Order Reduction Technique

“…The aim of MOR is to find a fairly accurate lower order approximate model which retains the essential properties of the original system like stability, passivity and input-output behaviour [1]- [5]. Truncated balanced realization (TBR) [6] is one of the most popular MOR techniques due to its accuracy, preservation of stability and easily computable a priori error bound.…”