Title :
Balanced truncation for time-delay systems via approximate Gramians
Author :
Wang, Xiang ; Wang, Qing ; Zhang, Zheng ; Chen, Quan ; Wong, Ngai
Author_Institution :
Dept. of Electr. & Electron. Eng., Univ. of Hong Kong, Hong Kong, China
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.
Keywords :
Lyapunov methods; RLC circuits; approximation theory; circuit complexity; circuit simulation; controllability; delays; observability; reduced order systems; Lyapunov-type equation; RLC network; TDS; approximate Gramian; balanced truncation; circuit simulation; computational complexity; controllability Gramians; model order reduction scheme; observability Gramians; reduced-order model; time-delay system; Approximation methods; Controllability; Delay; Equations; Mathematical model; Observability; Read only memory;
Conference_Titel :
Design Automation Conference (ASP-DAC), 2011 16th Asia and South Pacific
Conference_Location :
Yokohama
Print_ISBN :
978-1-4244-7515-5
DOI :
10.1109/ASPDAC.2011.5722251
