L2 gain verification for interconnections of locally stable systems using integral quadratic constraints

The paper establishes conditions which certify a local L₂ gain for interconnections of locally stable systems. The approach involves improvements to local L₂ gain estimation using reachability calculations. From these improved calculations, families of local integral quadratic constraints (IQCs) can be obtained for a fixed nonlinear dynamical system. Finally, the local IQCs are used to establish a local L₂ gain using a state-space formulation of the IQC robust performance theorem.