P
Passivity and Passivity Indices
for Switched and
Cyber-Physical Systems
Hasan Zakeri and Panos J. Antsaklis
Electrical Engineering Department, University
of Notre Dame, Notre Dame, IN, USA
Abstract
Cyber-physical systems (CPS), in which the
interactions with the environment are enabled
by computational and communication com-
ponents, 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 phys-
ical world. Given the large scale of such sys-
tems, 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 quan-
tify the “energy” consumption of a dynami-
cal 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. Passiv-
ity indices and passivation methods are also
discussed for linear, nonlinear, hybrid, and
networked systems.
Keywords
Passivity Passivity indices Dissipativity
Switched systems Hybrid systems
Cyber-physical systems Passivation
Introduction
This entry extends the discussion in the com-
panion entry Passivity, Dissipitativity, and Pas-
sivity Indices to the cases of switched and cyber-
physical systems. Passivity-based tools have been
studied for linear and nonlinear systems for a long
time, but their extension to switched and cyber-
physical systems is subject of recent research.
This extension provides tools to analysis and
design complex systems in a simpler manner.
Definitions of passivity indices and their
basic properties given in the companion entry
are extended here. Specific values of the
passivity indices of a system can be assigned
via compensation and can be used in design
approaches that involve not only passive but also
nonpassive systems. A review of design tools
based on passivation is also included.
© Springer-Verlag London Ltd., part of Springer Nature 2020
J. Baillieul, T. Samad (eds.), Encyclopedia of Systems and Control,
https://doi.org/10.1007/978-1-4471-5102-9 100147-1