Encyclopedia of Systems and Control

Living Edition
| Editors: John Baillieul, Tariq Samad

Passivity, Dissipativity and Passivity Indices

  • Hasan Zakeri
  • Panos J AntsaklisEmail author
Living reference work entry
DOI: https://doi.org/10.1007/978-1-4471-5102-9_100166-1


Passivity and dissipativity are energy-like concepts, widely used in control design, that capture the “energy” consumption of a dynamical system and therefore relate closely to the physical world. Passivity indices of a system are measures of its passivity margins and represent shortage and excess of passivity in a system. With the aid of passivity indices, one can measure how passive a system is, or how far from passivity it is. Passivity indices extend all the analysis and design methods based on passivity to nonpassive systems as well. One of the advantages of using passivity is its tight relationship to stability. Another is its compositionality, which, together with its generality, makes it possible to use passivity in a wide range of complex control systems. In the present entry, an overview of dissipativity and passivity is given. Passivity indices of a system and their relation to stability are defined, and methods to find the indices are presented.


Passivity Passivity indices Dissipativity Stability Energy 
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Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2020

Authors and Affiliations

  1. 1.Electrical Engineering DepartmentUniversity of Notre DameNotre DameUSA

Section editors and affiliations

  • Panos J. Antsaklis
    • 1
  1. 1.Department of Electrical EngineeringUniversity of Notre DameNotre DameUSA