A small-gain feedback interconnection for bilinear systems

Recently it has been shown that general bilinear systems satisfy a nonlinear L2-gain property, which is a qualitatively equivalent special case of the more general integral input-to-state stability (iISS) property. By exploiting a small-gain theorem that attends this nonlinear L2-gain property, a nontrivial example of a feedback interconnection for general bilinear systems is constructed that preserves this nonlinear L2-gain property, and hence iISS, in closed loop.