L2 controller synthesis with L∞-bounded closed-loop impulse response

In this paper we consider an L₂ control problem with an L_∞ norm on the closed-loop impulse response. To do this we first construct an upper bound for the L_∞ norm of the closed-loop system. To perform controller synthesis, we then modify the standard LQG cost functional by including an additional penalty term that weights the L_∞ norm of the impulse response of the closed-loop system. A numerical example is given to illustrate the improved L_∞ response of the closed-loop system.