Coprime factorization and optimal control on the doubly infinite discrete time axis

Reference:

Opmeer, M. R. and Staffans, O. J., 2012. Coprime factorization and optimal control on the doubly infinite discrete time axis. SIAM Journal on Control and Optimization (SICON), 50 (1), pp. 266-285.

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Official URL:

http://dx.doi.org/10.1137/110823742

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.

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