Factorization and the Nehari theorem in time-varying systems

The Nehari Theorem and related results on operator interpolation play an important role in modern system theory. These results are embedded in a function-theoretic conceptual framework and therefore restricted to LTI systems. We give a state space oriented extension of the Nehari Theorem to a time-varying system-theoretic setting. In that setting the theorem addresses the issue of measuring the distance between a noncausal bounded I/O operator and the family of causal I/O operators in stable linear systems. The analysis is based on the recent time-domain LQ optimization approach to robust control. The discussion includes a geometrical analysis of stable and antistable invariant subspaces, a short study of certain types of co-prime factorizations of I/O operators in time-varying systems, and a parametrization of all suboptimal solutions.The research was supported in part by the National Science Foundation under Grant ECS 9108927 and by the U.S. Army Research Office under Contract DAALO3 92 G 0015.The research was supported by NSERC, Canada.