Thermodynamics and large-scale nonlinear dynamical systems: A vector dissipative systems approach

Recent technological demands have required the analysis and control design of increasingly complex, large-scale nonlinear dynamical systems. In analyzing these largescale systems, it is often desirable to treat the overall system as a collection of interconnected subsystems. Solution properties of the large-scale system are then deduced from the solution properties of the individual subsystems and the nature of the system interconnections. In this paper we develop an energy flow modeling framework for large-scale dynamical systems based on vector dissipativity notions. Specifically using vector storage functions and vector supply rates, dissipativity properties of the composite large-scale system are shown to be determined from the dissipativity properties of the subsystems and their interconnections. Thermodynamic principles are also established using a large-scale systems perspective.