In this note, a novel barrier storage function
approach is developed to solve the L2–gain control problem for nonlinear control-affine systems under functional-inequality state constraints. The existence of barrier storage functions is shown to be sufficient for guaranteeing the existence of state-constrained
L2–gain controllers. Sufficient conditions for the existence of barrier storage functions are derived. Finally, a numerical example is given for illustration.
IEEE TRANSACTIONS ON AUTOMATIC CONTROL 65(2), p.771-777