Worst Case System Identification in l1: Optimal Algorithms and Error Bounds

This paper analyzes worst case identification of linear shift invariant systems with an l1 error criterion. A characterization of optimal algorithms and intrinsic errors of identification is given. The application of this characterization is made to identification in l1. The assumed apriori information on the plant are bounds on the system gain and decay rate of the impulse response of the unknown system and the experimental data is assumed to be a finite set of corrupted impulse or step response samples of the systems. Comparisons are made with the H¿ system identification problem. Comments on the l1 identification of small signal models of smooth nonlinear discrete time systems are made.