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

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Abstract

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.

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Authors and Affiliations

  1. College of Information Science and Technology, Donghua University, Shanghai, 201620, P.R. China

    Wuneng Zhou, Dongbing Tong & Jian’an Fang

  2. Key Laboratory of Wireless Sensor Network & Communication, Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences, Shanghai, 200050, P.R. China

    Wuneng Zhou

  3. School of Electronic Information and Control Engineering, Shandong Institute of Light Industry, Shandong, 250353, P.R. China

    Hongqian Lu

  4. Dept. of Aeronautical and Automotive Engineering, Loughborough University, Leicestershire, LE11 3TU, UK

    Qingchang Zhong

Authors
  1. Wuneng Zhou
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  2. Dongbing Tong
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  3. Hongqian Lu
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  4. Qingchang Zhong
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  5. Jian’an Fang
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Correspondence to Wuneng Zhou.

Additional information

This work is partially supported by the National “863” Key Program of China (2008AA042902), the National Natural Science Foundation of China (61075060, 60874113), the Doctor Base Foundation of Colleges and Universities by the Ministry of Education of China (200802550007), the Key Scientific Research, Innovation Program of Shanghai Education Committee (09zz66), the Key Basic Research Program of Shanghai City (09JC1400700), and the open project of State Key Laboratory of Industrial Control Technology (ICT1007).

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Zhou, W., Tong, D., Lu, H. et al. Time-Delay Dependent H ∞ Model Reduction for Uncertain Stochastic Systems: Continuous-Time Case. Circuits Syst Signal Process 30, 941–961 (2011). https://doi.org/10.1007/s00034-010-9245-x

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  • DOI: https://doi.org/10.1007/s00034-010-9245-x

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