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H ∞ reference tracking control design for a class of nonlinear systems with time-varying delays

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Abstract

This paper investigates the H ∞ trajectory tracking control for a class of nonlinear systems with time-varying delays by virtue of Lyapunov-Krasovskii stability theory and the linear matrix inequality (LMI) technique. A unified model consisting of a linear delayed dynamic system and a bounded static nonlinear operator is introduced, which covers most of the nonlinear systems with bounded nonlinear terms, such as the one-link robotic manipulator, chaotic systems, complex networks, the continuous stirred tank reactor (CSTR), and the standard genetic regulatory network (SGRN). First, the definition of the tracking control is given. Second, the H ∞ performance analysis of the closed-loop system including this unified model, reference model, and state feedback controller is presented. Then criteria on the tracking controller design are derived in terms of LMIs such that the output of the closed-loop system tracks the given reference signal in the H ∞ sense. The reference model adopted here is modified to be more flexible. A scaling factor is introduced to deal with the disturbance such that the control precision is improved. Finally, a CSTR system is provided to demonstrate the effectiveness of the established control laws.

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Authors and Affiliations

  1. State Key Laboratory of Industrial Control Technology, Zhejiang University, Hangzhou, 310027, China

    Mei-qin Liu

  2. College of Electrical Engineering, Zhejiang University, Hangzhou, 310027, China

    Mei-qin Liu, Hai-yang Chen & Sen-lin Zhang

Authors
  1. Mei-qin Liu
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  2. Hai-yang Chen
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  3. Sen-lin Zhang
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Correspondence to Mei-qin Liu.

Additional information

Project supported by the National Natural Science Foundation of China (Nos. 61222310, 61174142, and 61374021), the Zhejiang Provincial Natural Science Foundation of China (No. LZ14F030002), the Specialized Research Fund for the Doctoral Program of Higher Education of China (Nos. 20120101110115 and 20130101110109), and the Fundamental Research Funds for the Central Universities, China (No. 2014XZZX003-12)

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Liu, Mq., Chen, Hy. & Zhang, Sl. H ∞ reference tracking control design for a class of nonlinear systems with time-varying delays. Frontiers Inf Technol Electronic Eng 16, 759–768 (2015). https://doi.org/10.1631/FITEE.1500053

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  • DOI: https://doi.org/10.1631/FITEE.1500053

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