Multivariable Nehari problem and interpolation

Entropy and Multivariable Interpolation

We define a new notion of entropy for operators on Fock spaces and positive definite multi-Toeplitz kernels on free semigroups. This is studied in connection with factorization theorems for (multi-Toeplitz, multi-analytic, etc.) operators on Fock spaces. These results lead to entropy inequalities and entropy formulas for positive definite multi-Toeplitz kernels on free semigroups (resp. multi-T...

Multivariable Interpolation Problems

Coefficient stripping in the matricial Nehari problem

This note deals with a matricial Schur function arising from a completely indeterminate Nehari problem. The Schur algorithm is characterized by a unilateral shift for a Nehari sequence. c ⃝ 2017 Elsevier Inc. All rights reserved. MSC: 42C05; 42A56; 42A70

Multivariable deadbeat servo problem

The problem of tracking a reference vector variable from a given class is considered for discrete-time linear multi-input-output plants. The plant and the reference are both described by an input/output relation and the objective is to track exactly in a minimum number of steps. The optimal control law is shown to contain both feedback and feedforward terms and it is obtained by solving only th...

The Suboptimal Nehari Problem for Well-Posed Linear Systems

We solve the suboptimal Nehari problem for a transfer function that has a state-space realization as a system-stable (input, output and inputoutput stable) well-posed linear system. We obtain an explicit solution in terms of the state-space parameters.