COPRIME FACTORIZATION AND OPTIMAL CONTROL ON THEDOUBLY INFINITE DISCRETE TIME AXIS

摘要

We study the problem of strongly coprime factorization over H-infinity of the unitdisc. We give a necessary and sufficient condition for the existence of such a coprime factorizationin terms of an optimal control problem over the doubly infinite discrete-time axis. In particular, weshow that an equivalent condition for the existence of such a coprime factorization is that both thecontrol and filter algebraic Riccati equation (of an arbitrary realization) have a solution (in generalunbounded and even nondensely defined) and that a coupling condition involving these solutions issatisfied.