On L1 optimal control

It is shown that the problem of minimizing the effect of the worst disturbance on the output, where the signals have finite one norms, is equivalent to the same problem with bounded disturbances. The following situations provide the motivation to study such a problem. (1) Disturbances are generated by a fixed bounded-input, bounded-output (BIBO) stable, linear time-invariant (LTI) system with unknown initial conditions and zero input. (The output of this fixed system is the disturbance input to the original control system). (2) Disturbances are generated by an unknown BIBO stable LTI system whose fixed input consists of the unit impulse (this is the dual of (1)). In both of these situations, the disturbances will have a finite one norm