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.
Sensitive dependence on parameters of continuous-time nonlinear dynamical systems