# Large-Scale Continuous-Time Interconnected Dynamical Systems

# Large-Scale Continuous-Time Interconnected Dynamical Systems

This chapter extends classical dissipativity theory to vector dissipativity for addressing large-scale continuous-time interconnected dynamical systems using vector storage functions and vector supply rates. In particular, it develops an energy flow modeling framework for large-scale dynamical systems based on vector dissipativity notions. Using vector storage functions and vector supply rates, the chapter shows that the dissipativity properties of a composite large-scale system are determined from the dissipativity properties of the subsystems and their interconnections. It also derives extended Kalman–Yakubovich–Popov equations, in terms of the subsystem dynamics and interconnection constraints, characterizing vector dissipativeness via vector system storage functions. In addition, feedback interconnection stability results are developed for large-scale nonlinear dynamical systems using vector Lyapunov functions. These results are specialized to passive and nonexpansive large-scale dynamical systems.

*Keywords:*
dissipativity theory, vector dissipativity, interconnected dynamical system, vector storage function, vector supply rate, energy flow, Kalman–Yakubovich–Popov equations, feedback interconnection stability, vector Lyapunov function, dynamical system

Princeton Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us.