Commutant lifting for linear time-varying systems

In this paper, we study two robust control problems for possibly infinite dimensional (i.e., systems with an infinite number of states) linear time-varying (LTV) systems using a framework based on a version of the commutant lifting theorem developed for nest algebras. The approach is purely operator theoretic and does not use any state space representation. The two problems studied include the optimal disturbance attenuation and the optimal mixed sensitivity problems for LTV systems. The proposed solutions are given in terms of projections of time-varying multiplication operators. The latter are computed explicitly.