Rational ℒ1 compensators with ℋ∞ constraints

This paper presents a rational L₁ and mixed L ₁/ℋ_∞ compensator design methodology for continuous time systems. The problem formulation involves finding a finite dimensional stabilizing feedback controller that minimizes the L1 norm of a closed-loop transfer matrix subject to a frequency domain ℋ_∞ norm constraint on another closed-loop transfer matrix. It is shown that for a one-block problem the optimal solution can be approximated arbitrarily closely in terms of the closed-loop L₁ norm, by solving a sequence of convex optimization problems over linear matrix inequalities. Numerical example is provided to demonstrate the effectiveness of this approach