in this paper, the disturbance attenuation properties for classes of linear hybrid systems perturbed by exterior disturbances are investigated, and a hybrid l1 robust optimal control problem is studied. First, a procedure is developed to determine the minimal l∞ induced gain of linear hybrid systems. However, for general hybrid systems, the termination of the procedure is not guaranteed. Then, the decidability issues are briefly discussed. Finally, we study the robust l1 optimal controller synthesis problem. It is shown that the optimal performance level can be achieved by a piecewise linear state feedback control law for the linear hybrid systems, and a systematic approach to design such feedback control is proposed.