Model Order Reduction for Neutral Systems by Moment Matching
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Model Order Reduction for Neutral Systems by Moment Matching Qing Wang · Yuanzhe Wang · Edmund Y. Lam · Ngai Wong
Received: 8 August 2011 / Revised: 17 August 2012 / Published online: 11 September 2012 © The Author(s) 2012. This article is published with open access at Springerlink.com
Abstract Circuits with delay elements are very popular and important in the simulation of very-large-scale integration (VLSI) systems. Neutral systems (NSs) with multiple constant delays (MCDs), for example, can be used to model the partial element equivalent circuits (PEECs), which are widely used in high-frequency electromagnetic (EM) analysis. In this paper, the model order reduction (MOR) problem for the NS with MCDs is addressed by moment matching method. The nonlinear exponential terms coming from the delayed states and the derivative of the delayed states in the transfer function of the original NS are first approximated by a Padé approximation or a Taylor series expansion. This has the consequence that the transfer function of the original NS is exponential-free and the standard moment matching method for reduction is readily applied. The Padé approximation of exponential terms gives an expanded delay-free system, which is further reduced to a delay-free reduced-order model (ROM). A Taylor series expansion of exponential terms lets the inverse in the original transfer function have only powers-of-s terms, whose coefficient matrices are of the same size as the original NS, which results in a ROM modeled by a lower-order NS. Numerical examples are included to show the effectiveness of the proposed alQ. Wang () · Y. Wang · E.Y. Lam · N. Wong Department of Electrical and Electronic Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong, Hong Kong e-mail: [email protected] E.Y. Lam e-mail: [email protected] N. Wong e-mail: [email protected] Y. Wang Carnegie Mellon University Pittsburgh, 5000 Forbes Avenue, Hamerschlag Hall, Pittsburgh, PA, 15213 USA e-mail: [email protected]
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Circuits Syst Signal Process (2013) 32:1039–1063
gorithms and the comparison with existing MOR methods, such as the linear matrix inequality (LMI)-based method. Keywords Reduction · Moment · Time delay · Neutral system · Descriptor system
1 Introduction To describe the behavior of complex physical systems accurately, high or even infinite order mathematical models are often required. However, direct simulation of the original high or even infinite order models is very difficult and sometimes prohibitive due to unmanageable levels of storage, high computational cost and long computation time. Therefore, model order reduction (MOR) , which replaces the original complex and high-order system by a reduced-order model (ROM), plays an important role in many areas of engineering, e.g., transmission lines in circuit packaging [31, 38], PCB (printed circuit board) design [11, 48, 58] and networked control systems [18, 28]. The obvious advantages of MOR include that the use of ROMs results in not only considerable savings in storage and computational
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