SUMMARYA generalized g-level H 1 sub-optimal input decoupling (SOID) filtering problem is formulated. It is a generalization of g-level H 1 SOID filtering problem when, besides an input with unknown statistical properties but with a finite RMS norm, there exists an additional input to the given plant or system. The additional input is a linear combination of sinusoidal signals each of which has an unknown amplitude and phase but known frequency. The analysis, design, and performance limitations of generalized H 1 optimal filters are presented.