Subspace-based rational interpolation of analytic functions from phase data
IEEE Transactions on Signal Processing
Automatica (Journal of IFAC)
| Hi-index | 0.01 |
This paper describes the modification of the family of {\sc moesp}\footnote{The acronym {\sc moesp} stands for multivariable output error state--space model identification schemes and was introduced in \cite{jc1}.} subspace algorithms when identifying mixed causal and anti-causal systems. It is assumed that these class of systems have a regular pencil $zE - A$, where $E$ is possibly singular. The key numerical problem in solving this identification problem is the separation of the extended observability matrix of the causal part from that of the anti-causal part when a mixture of both is determined from the input--output data. For the general mixed causal, anti-causal case, this requires a partial calculation of the Kronecker canonical form of the pencil $zE - A$, where the pair $[A \; E]$ has been determined from the recorded input--output data. For the descriptor case, that is, when $E$ is nilpotent, this problem is solved without computing the Kronecker canonical form. All existing members of the {\sc moesp} family applicable to causal, linear, time-invariant systems are generalized. This allows a broad scope of identification problems for mixed causal, anti-causal systems to be addressed.