Sparse Identification of Fractional Transfer Functions

We consider the identification problem of a real coefficient rational transfer function from a small number of frequency domain measurements. By introducing an auxiliary transfer function with sufficiently large order, the identification problem can be formulated as a compressed sensing framework where the coefficient is the sparse vector to be reconstructed. Then
$l_{1}$
minimization can be used to reconstruct the coefficient and order simultaneously. We prove that the sensing matrix behaves like the union of partial sub-unitary matrices, which guarantees that
$l_{1}$
minimization can reconstruct the coefficient with high probability. The simulation experimental results have demonstrated the effectiveness and accuracy of the proposed method.