On Causal Commutant Lifting Theorems

A causal commutant lifting theorem has been given for time-invariant operators (Foias and Tannenbaum, to appear in J. Funct. Anal.). In this paper we prove certain causal lifting theorems for time-varying operators. Namely, we consider causal lifting without time-invariance or causal m-periodic lifting. Also by using these results we solve some causal H∞-optimization problems arising in non-linear system control.