Stability conditions for constrained two-stage internal model control

A robust stability test for a two-stage internal model control (IMC) antiwindup is presented. The two-stage IMC antiwindup scheme guarantees optimal closed loop performance both at transient and at steady state by solving two quadratic programs (QPs) online at each time step. The controller input-output mappings satisfy certain integral quadratic constraints (IQCs) and thus robust stability conditions can be constructed against any infinity-norm bounded uncertainty. The test is illustrated for a two-input two-output plant with left matrix fraction uncertainty.