Stability margins in inverse optimal input-to-state stabilization

We show that if a system is input-to-state stabilizable, we can always design a controller that is input-to-state stabilizing if the presence of input unmodeled dynamics of the form a(I+P) where a⩾1/2 is constant and P is a strictly passive (possibly nonlinear) system. This result is a direct extension to nonlinear systems with disturbances of the well known inverse optimality result from linear systems (infinite gain margin and 60° phase margins)