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Quantized stabilization of strict-feedback nonlinear systems based on ISS cyclic-small-gain theorem

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Abstract

This paper proposes a new tool for quantized nonlinear control design of dynamic systems transformable into the dynamically perturbed strict-feedback form. To address the technical challenges arising from measurement and actuator quantization, a new approach based on set-valued maps is developed to transform the closed-loop quantized system into a large-scale system composed of input-to-state stable (ISS) subsystems. For each ISS subsystem, the inputs consist of quantization errors and interacting states, and moreover, the ISS gains can be assigned arbitrarily. Then, the recently developed cyclic-small-gain theorem is employed to guarantee input-to-state stability with respect to quantization errors and to construct an ISS-Lyapunov function for the closed-loop quantized system. Interestingly, it is shown that, under some realistic assumptions, any n-dimensional dynamically perturbed strict-feedback nonlinear system can be globally practically stabilized by a quantized control law using 2n three-level dynamic quantizers.

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Authors and Affiliations

  1. Department of Electrical and Computer Engineering, Polytechnic Institute of New York University, Brooklyn, NY, 11201, USA

    Tengfei Liu & Zhong-Ping Jiang

  2. School of Electrical and Information Engineering, The University of Sydney, Sydney, NSW, 2006, Australia

    David J. Hill

Authors
  1. Tengfei Liu
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  2. Zhong-Ping Jiang
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  3. David J. Hill
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Corresponding author

Correspondence to Tengfei Liu.

Additional information

This research was supported in part under the Australian Research Councils Discovery funding scheme (project number: FF0455875), in part by a seed grant from NYU and POLY, and by NSF grant DMS-0906659.

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Liu, T., Jiang, ZP. & Hill, D.J. Quantized stabilization of strict-feedback nonlinear systems based on ISS cyclic-small-gain theorem. Math. Control Signals Syst. 24, 75–110 (2012). https://doi.org/10.1007/s00498-012-0079-x

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  • DOI: https://doi.org/10.1007/s00498-012-0079-x

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