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