Large-scale nonlinear models arise in many applications such as network control, biological system, aerospace, etc. Certificates to validate properties such as stability regions are desirable. However, analysis with certificates of high-order nonlinear systems' behavior is difficult, even with polynomial vector fields.
We propose two approaches to tackle this difficulty. The first involves a study of a specific class of passive systems with gain roll-off at high frequency. Using integral quadratic constraints to encapsulate system properties, we achieve a bound on the relationship between the maximum allowable time delay and the overall gain of the system. In a specific case, we present a closed form stability criterion.
The second approach assumes that the dynamics of the interconnection are known. We decompose the system into smaller subsystems, establish coarse properties of those subsystems using integral quadratic constraints, and analyze the interconnection using only the coarse properties. We present an example in which we achieve a superior bound than the standard, polynomial certificate technique.