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

Abstract

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.

Keywords

Passivity Passivity indices Dissipativity Stability Energy 
This is a preview of subscription content, log in to check access.

Bibliography

  1. Antsaklis PJ, Goodwine B, Gupta V, McCourt MJ, Wang Y, Wu P, Xia M, Yu H, Zhu F (2013) Control of cyberphysical systems using passivity and dissipativity based methods. Eur J Control 19(5):379–388CrossRefGoogle Scholar
  2. Bao J, Lee PL (2007) Process control: the passive systems approach. Advances in industrial control. Springer, LondonGoogle Scholar
  3. Haddad WM, Chellaboina V (2008) Nonlinear dynamical systems and control: a Lyapunov-based approach. Princeton University Press, PrincetonCrossRefGoogle Scholar
  4. Hill D, Moylan P (1976) The stability of nonlinear dissipative systems. IEEE Trans Autom Control 21(5): 708–711MathSciNetCrossRefGoogle Scholar
  5. Hill DJ, Moylan PJ (1980) Dissipative dynamical systems: basic input-output and state properties. J Frankl Inst 309(5):327–357MathSciNetCrossRefGoogle Scholar
  6. Khalil HK (2002) Nonlinear systems, 3rd edn. Prentice Hall, Upper Saddle RiverzbMATHGoogle Scholar
  7. Kottenstette N, McCourt MJ, Xia M, Gupta V, Antsaklis PJ (2014) On relationships among passivity, positive realness, and dissipativity in linear systems. Automatica 50(4):1003–1016MathSciNetCrossRefGoogle Scholar
  8. Romer A, Montenbruck JM, Allgöwer F (2018) Some ideas on sampling strategies for data-driven inference of passivity properties for MIMO systems. In: American Control Conference (ACC), 2018, Milwaukee, pp 6094–6100Google Scholar
  9. van der Schaft A (2017) L2-gain and passivity techniques in nonlinear control. Communications and control engineering. Springer International Publishing, ChamCrossRefGoogle Scholar
  10. Willems JC (1972) Dissipative dynamical systems part I: general theory. Arch Ration Mech Anal 45(5):321–351CrossRefGoogle Scholar
  11. Xia M, Antsaklis PJ, Gupta V, McCourt MJ (2015) Determining passivity using linearization for systems with feedthrough terms. IEEE Trans Autom Control 60(9):2536–2541MathSciNetCrossRefGoogle Scholar
  12. Zakeri H, Antsaklis PJ (2019a) A data-driven adaptive controller reconfiguration for fault mitigation: a passivity approach. In: 2019 27th Mediterranean Conference on Control and Automation (MED), pp 25–30Google Scholar
  13. Zakeri H, Antsaklis PJ (2019b) Passivity and passivity indices of nonlinear systems under operational limitations using approximations. arXiv:190100852 [cs] 1901.00852Google Scholar
  14. Zakeri H, Antsaklis PJ (2019c) Recent advances in analysis and design of cyber-physical systems using passivity indices. In: 2019 27th Mediterranean Conference on Control and Automation (MED), pp 31–36Google Scholar

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