L^{1}-optimal compensators for continuous-time systems

Previous work has been concerned with minimizing thel^{1}-norm of an error pulse response for discrete-time SISO [1] and MIMO [2] systems. In this paper we study the problem of minimizing the L¹-norm of the error impulse response for SISO continuous-time systems. This problem is quite different from the discrete-time problem in that irrational solutions are obtained even when the problem data are rational. Two methods are suggested for the solution of the continuous-time problem; an exact method which leads to a finite-dimensional nonlinear programming problem, and an approximate method which leads to a linear programming problem.