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Asynchronous Switched Systems: ADT Switching

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Time-Dependent Switched Discrete-Time Linear Systems: Control and Filtering

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 53))

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Abstract

This chapter first investigates the stability and \(l_2\)-gain analysis problems for a class of discrete-time switched systems with average dwell time (ADT) switching by allowing the Lyapunov-like functions to increase during the running time of subsystems. The obtained results then facilitate the studies on the issues of asynchronous control, where “asynchronous ” means the switching of the controllers has a lag to the switching of system modes. The basic asynchronous stabilization and asynchronous \(H_\infty \) control problem are both studied and the case for the system with time-varying parameter is further addressed under the modal average dwell time (MADT). Finally, the asynchronous \(H_\infty \) filter design problem is dealt with for the underlying switched linear systems with ADT switching. The phenomenon of “asynchronous” switching will unavoidably deteriorate the control performance such as the \(H_\infty \) noise attenuation index. However, it can be verified that the designed controller/filter considering the synchronous switching will be not necessarily valid in the presence of asynchronous switching. Several examples are provided to show the potential of the developed results.

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Authors and Affiliations

  1. School of Astronautics, Harbin Institute of Technology, Harbin, China

    Lixian Zhang & Yanzheng Zhu

  2. School of Electrical and Electronic Engineering, The University of Adelaide, Adelaide, Australia

    Peng Shi

  3. Department of Chemical and Biological Engineering, The University of British Columbia, Vancouver, BC, Canada

    Qiugang Lu

  4. College of Engineering and Science, Victoria University, Melbourne, VIC, Australia

    Peng Shi

Authors
  1. Lixian Zhang
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  2. Yanzheng Zhu
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  3. Peng Shi
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  4. Qiugang Lu
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Correspondence to Lixian Zhang .

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Zhang, L., Zhu, Y., Shi, P., Lu, Q. (2016). Asynchronous Switched Systems: ADT Switching. In: Time-Dependent Switched Discrete-Time Linear Systems: Control and Filtering. Studies in Systems, Decision and Control, vol 53. Springer, Cham. https://doi.org/10.1007/978-3-319-28850-5_6

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  • DOI: https://doi.org/10.1007/978-3-319-28850-5_6

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-28849-9

  • Online ISBN: 978-3-319-28850-5

  • eBook Packages: EngineeringEngineering (R0)

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