  We show that designing sparse $H_\infty$ controllers, in a discrete (LTI)
setting, is easy when the controller is assumed to be an FIR filter. In this
case, the problem reduces to a static output feedback problem with equality
constraints. We show how to obtain an initial guess, for the controller, and
then provide a simple algorithm that alternates between two (convex)
feasibility programs until converging, when the problem is feasible, to a
suboptimal $H_\infty$ controller that is automatically stable. As FIR filters
contain the information of their impulse response in their coefficients, it is
easy to see that our results provide a path of least resistance to designing
sparse robust controllers for continuous-time plants, via system identification
methods.
