Abstract
The extended ( J, J ′)-lossless factorization for discrete-time rational matrix functions with zeros on the unit circle is considered. A necessary and sufficient condition for the existence of the extended ( J, J ′)-lossless factorization is obtained. The condition is given in terms of the original system parameters in the form of a generalized eigenvalue problem and a discrete-time algebraic Riccati equation. State-space representations for the extended ( J, J ′)-lossless factorization are provided.
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