Robust Stability of Positive Monotone Feedback Interconnections

Positive monotonicity and robustness of feedback interconnections of nonlinear systems are studied. First, it is shown that a well-known instantaneous gain condition on the open-loop systems, which implies feedback well-posedness, also guarantees feedback positivity. Second, parallel to the well-known results based on integral quadratic constraints, uncertainty in positive monotone feedback interconnections is characterized using a generalized notion of integral linear constraints (ILCs), which leads to robust stability conditions that are scalable with the dimensions of the systems. A list of ILCs for commonly encountered uncertainties is provided. The efficacy of the results is illustrated by a number of examples.