Controller Design via Infinite-Dimensional Linear Programming

This paper addresses the problem of synthesizing controllers to meet specifications that can be represented in terms of linear constraints. A duality result for the problem of minimizing the l
1
norm of a closed loop map augmented with linear convex constraints is derived, and it is shown that under mild assumptions, there is no duality gap in the primal-dual programs. The utility of this result is shown through the solution of two problems: the no-overshoot problem, and minimizing the l
1
norm of a system subjected to frequency domain constraints.