Abstract
We study the problem of existence of weak right or left or strong coprime factorizations in H-infinity over the right half-plane of an analytic function defined and uniformly bounded on some right half-plane. We give necessary and sufficient conditions for the existence of such coprime factorizations in terms of an optimal control problem over the doubly infinite continuous-time axis. In particular, we show that an equivalent condition for the existence of a strong coprime factorization is that both the control and the filter algebraic Riccati equation (of an arbitrary well-posed realization) have a solution (in general unbounded and not even densely defined) and that a coupling condition involving these two solutions is satisfied.
Original language | English |
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Pages (from-to) | 1985-2015 |
Number of pages | 31 |
Journal | SIAM Journal on Control and Optimization |
Volume | 57 |
Issue number | 3 |
Early online date | 13 Jun 2019 |
DOIs | |
Publication status | Published - 2019 |