Modern computational tools for stability, performance, and safety certification are not scalable to large nonlinear systems. In this dissertation we propose a compositional analysis approach that takes advantage of the interconnected structure of many modern large-scale systems to solve this problem. Specifically, we pose the certification problem as a distributed optimization that searches over the input-output properties of each subsystem to certify a desired property of the interconnected system. The alternating direction method of multipliers (ADMM), a popular distributed optimization technique, is employed to decompose and solve this problem.

This approach is very general in that it allows us to search over a wide range of input-output properties for each subsystem. We demonstrate the use of dissipativity, equilibrium independent dissipativity (EID), and integral quadratic constraints (IQCs) to characterize the properties of the individual subsystems and the entire interconnection. Multiple examples showing the applicability and scalability of the approach are presented.

Furthermore, we demonstrate how symmetries in the interconnection topology can be exploited to further improve the computational efficiency and scalability of the distributed optimization problem. Unlike other symmetry reduction techniques this approach does not require the subsystems to be identical, but only to share input-output properties. Thus, it can be applied to many real world systems. We demonstrate these reduction techniques on a large-scale nonlinear example and a vehicle platoon example.

Finally, we present a passivity-based formation control strategy for multiple unmanned aerial vehicles (UAVs) cooperatively carrying a suspended load. This strategy is designed such that the input-output properties of the individual UAVs and the interconnection structure guarantee stability of the system under appropriate conditions. Specifically, we show that the system is stable for any configurations where the cables carrying the suspended load are in tension.