Compositional Design and Verification of Large-Scale Systems Using Dissipativity Theory: Determining Stability and Performance from Subsystem Properties and Interconnection Structures

A major problem for safety-critical engineering systems is to certify the required stability and performance properties using analytical and computational models of a physical system. The methods for such certification are severely limited in their scalability, that is, their ability to cope with a large number of physical components and the complexity of their interactions. Rather than tackling the system model as a whole, this article advocates a compositional approach that derives system-level guarantees from dissipativity properties of the subsystems and their interconnection structure. This method is particularly suitable when the subsystems are amenable to standard analytical and computational methods. However, a monolithic model of the interconnection is beyond the reach of these techniques. The results reviewed here were motivated by several application problems, such as resource allocation in communication networks, motion coordination in multiagent systems, and dynamical analysis of biochemical reaction networks. Several examples are drawn from these applications to illustrate the results.