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Delays and Interconnections: Methodology, Algorithms and Applications pp 99–114Cite as

A Small-Gain Method for the Design of Decentralized Stabilizing Controllers for Interconnected Systems with Delays

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Part of the book series: Advances in Delays and Dynamics ((ADVSDD,volume 10))

Abstract

In this chapter, the decentralized, practical input-to-state stabilization of a class of interconnected systems, affected by time-delays in both the internal variables and in the communication channels, is considered. The Artstein–Sontag methodology of control Lyapunov functions, extended to systems with delays by control Lyapunov-Krasovskii functionals, is exploited in connection with the small-gain methods for retarded systems. A constructive methodology for the design of decentralized control laws in the presence of actuator disturbances is provided. Control Lyapunov-Krasovskii functionals for only subsystems are considered, thus reducing the difficulty with respect to finding an overall functional. A decentralized controller is provided by means of a small-gain condition, by which practical input-to-state stability with respect to actuator disturbances is guaranteed. If the disturbances are bounded, the controller allows to drive the system variables to an arbitrarily small neighborhood of the origin, by suitably tuning a control parameter.

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Acknowledgements

The work of P. Pepe has been supported in part by the MIUR-PRIN 2009 grant N. 2009J7FWLX002 and by the Center of Excellence for Research DEWS, Italy. The work of Z. P. Jiang has been supported in part by the NSF under Grant ECCS-1501044.

Author information

Authors and Affiliations

  1. Department of Information Engineering, Computer Science, and Mathematics, University of L’Aquila, Via Vetoio (Coppito I), 67100, L’Aquila, Italy

    Pierdomenico Pepe

  2. Department of Systems Design and Informatics, Kyushu Institute of Technology, 680-4 Kawazu, Iizuka, 820-8502, Japan

    Hiroshi Ito

  3. Department of Electrical and Computer Engineering, Tandon School of Engineering, New York University, Six Metrotech Center, Brooklyn, NY, 11201, USA

    Zhong-Ping Jiang

Authors
  1. Pierdomenico Pepe
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  2. Hiroshi Ito
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  3. Zhong-Ping Jiang
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Corresponding author

Correspondence to Pierdomenico Pepe .

Editor information

Editors and Affiliations

  1. Laboratoire des Signaux et Systèmes, CNRS-CentraleSupèlec-Université Paris-Saclay, Gif-sur-Yvette, France

    Giorgio Valmorbida

  2. Laboratoire d’Analyse et d’Architecture de Systèmes-CNRS, Toulouse, France

    Alexandre Seuret

  3. Laboratoire des Signaux et Systèmes, CNRS-CentraleSupèlec-Université Paris-Saclay, Gif-sur-Yvette, France

    Islam Boussaada

  4. Mechanical and Industrial Engineering, Northeastern University, Boston, MA, USA

    Rifat Sipahi

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Pepe, P., Ito, H., Jiang, ZP. (2019). A Small-Gain Method for the Design of Decentralized Stabilizing Controllers for Interconnected Systems with Delays. In: Valmorbida, G., Seuret, A., Boussaada, I., Sipahi, R. (eds) Delays and Interconnections: Methodology, Algorithms and Applications. Advances in Delays and Dynamics, vol 10. Springer, Cham. https://doi.org/10.1007/978-3-030-11554-8_7

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