Encyclopedia of Systems and Control

Living Edition
| Editors: John Baillieul, Tariq Samad

Passivity and Passivity Indices for Switched and Cyber-Physical Systems

  • Hasan Zakeri
  • Panos J. AntsaklisEmail author
Living reference work entry
DOI: https://doi.org/10.1007/978-1-4471-5102-9_100147-1


Cyber-physical systems (CPS), in which the interactions with the environment are enabled by computational and communication components, pose great challenges in design and analysis for control engineers. The operation of these systems is monitored, coordinated, controlled, and integrated by a computing and communication core interacting with the physical world. Given the large scale of such systems, it is important to develop tools that can guarantee system level properties, such as stability, from the properties of individual components and their interactions. Passivity and dissipativity are energy-like concepts and widely used in control design. They quantify the “energy” consumption of a dynamical system and have shown great promise in the design of cyber-physical systems because of their compositionality properties (Antsaklis et al., Eur J Control 19(5):379–388, 2013). Passivity indices are measures of passivity and extend the applicability of passivity-based tools to nonpassive systems as well. In the present entry, an overview of applications of passivity and passivity indices in the design of cyber-physical systems is given. Passivity indices and passivation methods are also discussed for linear, nonlinear, hybrid, and networked systems.


Passivity Passivity indices Dissipativity Switched systems Hybrid systems Cyber-physical systems Passivation 
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© 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