Balanced truncation for time-delay systems via approximate Gramians

16th Asia and South Pacific Design Automation Conference (ASP-DAC 2011) Pub Date : 2011-01-25 DOI:10.1109/ASPDAC.2011.5722251

Xiang Wang, Qing Wang, Zheng Zhang, Quan Chen, N. Wong

引用次数: 21

Abstract

In circuit simulation, when a large RLC network is connected with delay elements, such as transmission lines, the resulting system is a time-delay system (TDS). This paper presents a new model order reduction (MOR) scheme for TDSs with state time delays. It is the first time to reduce a TDS using balanced truncation. The Lyapunov-type equations for TDSs are derived, and an analysis of their computational complexity is presented. To reduce the computational cost, we approximate the controllability and observability Gramians in the frequency domain. The reduced-order models (ROMs) are then obtained by balancing and truncating the approximate Gramians. Numerical examples are presented to verify the accuracy and efficiency of the proposed algorithm.

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时滞系统的近似格拉姆式平衡截断

在电路仿真中，当一个大的RLC网络与延迟元件(如传输线)连接时，所得到的系统是一个时延系统(TDS)。针对具有状态时滞的tds，提出了一种新的模型降阶方案。这是第一次使用平衡截断来降低TDS。导出了tds的lyapunov型方程，并对其计算复杂度进行了分析。为了减少计算量，我们在频域近似了可控性和可观察性格兰量。然后通过平衡和截断近似格兰式得到降阶模型(ROMs)。数值算例验证了该算法的准确性和有效性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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16th Asia and South Pacific Design Automation Conference (ASP-DAC 2011)

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