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 algorithms and the comparison with existing MOR methods, such as the linear matrix inequality (LMI)-based method.
Highlights
To describe the behavior of complex physical systems accurately, high or even infinite order mathematical models are often required
The moment matching method is used to get two different kinds of reduced-order model (ROM) to approximate a Neutral systems (NSs) with multiple constant delays (MCDs) depending on ways of approximating exponential terms in the transfer function of the original NS
The Padé approximation of exponential terms renders a delay-free system modeled by the high-order descriptor system (DS), with the obvious price to be paid of higher storage and computational complexity
Summary
To describe the behavior of complex physical systems accurately, high or even infinite order mathematical models are often required. The major contribution of this paper is the reduction of the NS with MCDs by first approximating the nonlinear exponential terms via Padé approximation or Taylor series expansion of the exponential terms The former results in an expanded-size, but exponential-free, state space which can be reduced by standard moment matching method. Whereas the latter effectively replaces the exponential terms by truncated Taylor series, this allows the inverse in the transfer function computation to be again exponential-free, but contains only powers-of-s terms whose coefficient matrices are of the same size as those of the original NS.
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