Abstract
The problem of the existence and design of an optimal observer is considered for linear discrete-time systems with unknown disturbances additive to the output. The optimal observer reconstructs the best estimate of the state at a given time with respect to the worst disturbances constrained to a ball in l 2. It is proved that an observability condition is necessary and sufficient for the existence of such an observer. An explicit formula for the optimal observer is derived (it includes the degenerate case when some of the outputs are disturbance free).