Normalized coprime representations for time-varying linear systems

Abstract

Copyright © 2010 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.By considering the behaviour of stabilizable and detectable, linear time-varying state-space models over doublyinfinite continuous time, we establish the existence of so-called normalized coprime representations for the system graphs; that is, stable and stably left (resp. right) invertible, image (resp. kernel) representations that are normalized with respect to the inner product on L²(−∞,∞); this is consistent with the notion of normalization used in the time-invariant setting. The approach is constructive, involving the solution of timevarying differential Riccati equations with single-point boundary conditions at either +∞ or −∞. The contribution lies in accommodating state-space models that may not define an exponential dichotomy