On the Takagi interpolation problem

This problem is a generalization of the tangential Takagi interpolation problem with simple multiplicities (in the following abbreviated with TIP), which was first studied in [20] as an extension of the well-known Nevanlinna-Pick interpolation problem (see [4, 14, 16, 18]). The TIP and the closely related Nudel‘man problem have been posed and solved following various approaches: in the discrete-time case (see [20] and [15]), in the context of interpolation with rational matrix functions in continuous-time as reported in the book [4], and with the generalized Beurling-Lax approach introduced in [5]. This paper examines some issues related to the existence and characterization of solutions of the TIP, following an approach based on the exact modeling ∗Department of Systems Engineering, Faculty of Engineering Science, Osaka University, 1-3 Machikaneyamamachi, Toyonaka, Osaka 560, Japan, fax no.: +81-6-6850-6341, e-mail: [email protected] †ISIS group, School of Electronics and Computer Science, University of Southampton, SO17 1BJ Southampton, United Kingdom [email protected]