The nonlinear L-2 anti-windup framework introduced in Teel and Kapor (1997) reduces the anti-windup synthesis problem to a state feedback synthesis problem for linear systems with input saturation and input matched L-2 disturbances. In this note, based on the structure proposed in that previous paper, we provide a linear matrix ineqaulity (LMI) formulation of high-performance anti-windup design for control systems with linear asymptotically stable plants. In particular, we first give a linear quadratic-based formulation of linear anti-windup compensation, in terms of the solution of a set of (always feasible) LMI constraints. Then, we propose a nonlinear scheduling technique, where hysteresis switching among a family of linear gains is employed for performance improvement. Both design techniques are demonstrated on an academic example.