Rank deficiency of a matrix is equivalent to the existence of an exact linear model for the data that composes the matrix. In the context of linear static models, the data matrix is unstructured and the corresponding modelling problem is an approximation of the data matrix by another matrix of a lower rank. In the context of linear time-invariant dynamic models, the appropriate data matrix is Hankel and the corresponding modelling problems becomes structured low-rank approximation.
Low-rank approximation has applications in:
We explain the application for system identification and present algorithms for solving the problem. In the unstructured case, an appropriate computational tool is the singular value decomposition. In the structured case, the problem is more involved and is currently solved by local optimisation methods.
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