Generalizing the Markov and covariance interpolation problem using input-to-state filters
Provides a more flexible interpolation framework for control and signal processing applications, but is an incremental extension of existing methods.
The paper generalizes the Markov and covariance interpolation problem to match expansions around multiple points in the disc, solving it via input-to-state filters with Lyapunov equations and generalized eigenvalue problems.
In the Markov and covariance interpolation problem a transfer function $W$ is sought that match the first coefficients in the expansion of $W$ around zero and the first coefficients of the Laurent expansion of the corresponding spectral density $WW^\star$. Here we solve an interpolation problem where the matched parameters are the coefficients of expansions of $W$ and $WW^\star$ around various points in the disc. The solution is derived using input-to-state filters and is determined by simple calculations such as solving Lyapunov equations and generalized eigenvalue problems.