Generalized inverses of the vandermonde matrix: Applications in control theory

In the literature of control and system theory, several explicit formulae appeared for solving square Vandermonde systems and computing the inverse of it. In the present paper, we will discuss and present analytically the generalized inverses of the rectangular and square Vandermonde matrix. These matrices have been appeared recently in an interesting control and system theory problem, where the change of the initial state of a linear descriptor system in (almost) zero time is required.

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