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Dynamic Dissipativity Theory for Stability of Time-Delay Systems

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Delays and Interconnections: Methodology, Algorithms and Applications

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

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Abstract

In this paper, we present new sufficient conditions for asymptotic stability of linear and nonlinear time delay dynamical systems using dynamic dissipativity theory. Specifically, we first show that the time delay operator is dissipative with a Lyapunov-Krasovskii-type storage function. Next, by representing a time delay dynamical system as a negative feedback interconnection of a finite-dimensional dynamical system and an infinite-dimensional time delay operator, we use the feedback interconnection of dynamic dissipative systems to derive sufficient conditions for stability of time-delay systems.

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Author information

Authors and Affiliations

  1. Mahindra École Centrale, Hyderabad, India

    Vijaysekhar Chellaboina

  2. Georgia Institute of Technology, Atlanta, GA, USA

    Wassim M. Haddad

Authors
  1. Vijaysekhar Chellaboina
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  2. Wassim M. Haddad
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Corresponding author

Correspondence to Vijaysekhar Chellaboina .

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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Chellaboina, V., Haddad, W.M. (2019). Dynamic Dissipativity Theory for Stability of Time-Delay Systems. 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_3

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