Time-Delay Dependent H∞ Model Reduction for Uncertain Stochastic Systems: Continuous-Time Case

• Published in: Circuits, systems, and signal processing Vol. 30; no. 5; pp. 941 - 961
• Main Authors: Zhou, Wuneng, Tong, Dongbing, Lu, Hongqian, Zhong, Qingchang, Fang, Jian’an
• Format: Journal Article
• Language: English
• Published: Boston SP Birkhäuser Verlag Boston 01.10.2011
• Subjects: Circuits and Systems; Electrical Engineering; Electronics and Microelectronics; Engineering; Instrumentation; Signal,Image and Speech Processing; Uncertainty; performance; Model reduction; Time delay; Stochastic system
• ISSN: 0278-081X; 1531-5878
• DOI: 10.1007/s00034-010-9245-x

The problem of robust H ∞ model reduction for uncertain stochastic systems with time delay is investigated in this paper. The attention of this paper is focused on the construction of a reduced-order model for a given stable system. Several sufficient conditions are obtained for ensuring the existence of the reduced-order model by means of linear matrix inequalities and a coupling non-convex rank constraint condition. Under the sufficient conditions, the desired reduced-order model can be constructed, and the error system between the original model and the reduced-order model is asymptotically stable and has a prescribed H ∞ performance. Based on the proposed method, the construction approaches of reduced-order models with special structures, such as the zeroth-order model, the delay-free model, and the no-parameter-uncertainties model, are also developed. Finally, the effectiveness of the proposed model reduction method is illustrated by a numerical simulation example.