State-Constrained Nonlinear $L_2$-Gain Control

In this note, a novel barrier storage function approach is developed to solve $L_{2}$ -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 $L_{2}$ -gain controllers. Sufficient conditions for the existence of barrier storage functions are derived. Finally, a numerical example is given for illustration.