Gramian-based model order reduction of parameterized time-delay systems

Time-delay systems (TDSs) frequently arise in circuit simulation especially in high-frequency applications. Model order reduction (MOR) techniques can be used to facilitate the simulation of TDSs. On the other hand, many kinds of variations, such as temperature and geometric uncertainties, can have significant impact on the transient responses of TDSs. Therefore, it is important to preserve parametric dependence during the MOR procedure. This paper presents a new parameterized MOR scheme for TDSs with parameter variations. We derive parameterized reduced-order models (ROMs) for TDSs using balanced truncation by approximating the Gramians in the multi-dimensional space of parameters. The resulting ROMs can preserve the parametric dependence, making it efficient for repeated simulations under different parameter settings. Numerical examples are presented to verify the accuracy and efficiency of our proposed algorithm. Copyright © 2012 John Wiley & Sons, Ltd. Received 19 July 2011; Revised 22 May 2012; Accepted 12 November 2012