Region of attraction comparison for gradient projection anti-windup compensated systems

The gradient projection anti-windup (GPAW) scheme was recently proposed for saturated multi-input-multi-output (MIMO) nonlinear systems driven by MIMO nonlinear controllers, a topic recognized as an open problem in a recent survey paper. Thus far, stability results for GPAW compensated systems are restricted to the simple case of a saturated first order linear time invariant (LTI) plant driven by a first order LTI controller. Here, we present a region of attraction (ROA) comparison result for general GPAW compensated regulatory systems. The ROA comparison result is demonstrated on a simple planar nonlinear system, which also highlights the limitations of existing state-of-the-art anti-windup results.