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Generalized inverses of the vandermonde matrix: Applications in control theory

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Abstract

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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Authors and Affiliations

  1. Institute for Financial and Actuarial Mathematics (IFAM), Department of Mathematical Sciences, and Institute for Risk and Uncertainty, University of Liverpool, Liverpool, UK

    Athanasios A. Pantelous

  2. Department of Mathematics, University of Athens, Panepistimioupolis, Athens, Greece

    Athanasios D. Karageorgos

Authors
  1. Athanasios A. Pantelous
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  2. Athanasios D. Karageorgos
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Correspondence to Athanasios A. Pantelous.

Additional information

Recommended by Editorial Board member Nam H. Jo under the direction of Editor Hyungbo Shim.

The authors are very grateful to the associate editor and the six anonymous referees’ comments, suggestions and remarks which have improved highly the quality of the paper.

Athanasios A. Pantelous received his B.S. and M.Sc. in Applied Mathematics, and Statistics & O.R. from the Department of Mathematics, University of Athens and his Ph.D. in Statistics (Actuarial Mathematics) from the Department of Statistics, Athens University of Economics and Business, Greece. Currently, he is a Reader in the Department of Mathematical Sciences, Director of the Institute for Financial and Actuarial Mathematics (IFAM), and member of the multidisciplinary Institute for Risk and Uncertainty (IR&U), University of Liverpool, UK. His research interests include linear (stochastic) control, descriptor (stochastic) systems, linear algebra, actuarial and financial mathematics.

Athanasios D. Karageorgos received his B.S., M.Sc. and Ph.D. degrees in Mathematics from the Department of Mathematics, University of Athens, Greece. His research interests include linear control, descriptor systems, linear algebra and their applications.

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Pantelous, A.A., Karageorgos, A.D. Generalized inverses of the vandermonde matrix: Applications in control theory. Int. J. Control Autom. Syst. 11, 1063–1070 (2013). https://doi.org/10.1007/s12555-012-0153-7

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  • DOI: https://doi.org/10.1007/s12555-012-0153-7

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