On causal commutant lifting theorems (Q1310874)

A causal commutant lifting theorem has been given for time-invariant operators by \textit{C. Foias} and \textit{A. Tannenbaum} [`Causality in commutant lifting theory', to appear in J. Funct. Anal.]. In this paper certain causal lifting theorems for time-varying operators are proved. Namely, causal lifting without time-invariance or causal \(m\)-periodic lifting is considered. Also by using these results some causal \(H^ \infty\)-optimization problems arising in nonlinear system control are solved.