Worst-case system identification in l1: error bounds, optimal models and model reduction

In l₁-robust control design, model uncertainty can be handled if an upper bound on the l₁-norm of the model error is known. A procedure is developed which yields such an upper bound for a given nominal model, using measurement data and a priori information consisting of a time-domain bound on the noise and information about the decay rate of the pulse response of the model error. The upper bound is calculated by solving a set of linear programming problems. Moreover, a procedure is presented for obtaining a new nominal model which is optimal in an l₁-sense, i.e., has a minimal upper bound on the l₁-norm of the model error. This is performed in two steps: in the first step the central estimate is computed, and in the second step model reduction in the l₁-norm is performed. For the latter problem, a solution is given for the case when the reduced-order model is linear in the parameters