Abstract
We study the problem of strongly coprime factorization over H-infinity of the unit disc. We give a necessary and sufficient condition for the existence of such a coprime factorization in terms of an optimal control problem over the doubly infinite discrete-time axis. In particular, we show that an equivalent condition for the existence of such a coprime factorization is that both the control and filter algebraic Riccati equation (of an arbitrary realization) have a solution (in general unbounded and even non densely defined) and that a coupling condition involving these solutions is satisfied.
Original language | English |
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Pages (from-to) | 266-285 |
Number of pages | 20 |
Journal | SIAM Journal on Control and Optimization |
Volume | 50 |
Issue number | 1 |
Early online date | 19 Jan 2012 |
DOIs | |
Publication status | Published - 2012 |