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Part of the book series: Power Systems ((POWSYS))

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Abstract

In this chapter, we complement our book by putting together some basic mathematical tools and analytical results that will help the reader in following up the contents of the different chapters. In this appendix, we collect some useful mathematical facts, inequalities, and lemmas which have been extensively used throughout the book.

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Notes

  1. 1.

    In some literature, an inner product is also called a dot product, denoted by \(u \cdot v\) . However, in this book, we will not use that name.

  2. 2.

    It is also called Sylvester equation in some literature.

References

  1. Ackermann J (1972) Fer Entwurf Linearer Regelungssysteme im Zustandsraum. Regelungstech, Prozess-Datenverarb 7:297–300

    Google Scholar 

  2. Angeli D, Bliman PA (2009) Convergence speed of unsteady distributed consensus: decay estimate along the settling spanning-trees. SIAM J Control Optim 48(1):1–32

    Article  MATH  MathSciNet  Google Scholar 

  3. Chiang RY, Safonov MG (1992) User’s guide, robust control toolbox. The MathWorks, Natick

    Google Scholar 

  4. Godsil C, Royle G (2001) Algebraic graph theory. Springer, New York

    Book  MATH  Google Scholar 

  5. Noble B, Daniel J (1988) Applied linear algebra, 3rd edn. Prentice Hall, New York

    Google Scholar 

  6. Olfati-Saber R, Murray R (2004) Consensus problems in networks of agents with switching topology and time delays. IEEE Trans Autom Control 49(9):1520–1533

    Article  MathSciNet  Google Scholar 

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Correspondence to Magdi S. Mahmoud .

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© 2015 Springer International Publishing Switzerland

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Mahmoud, M.S., AL-Sunni, F.M. (2015). Appendix. In: Control and Optimization of Distributed Generation Systems. Power Systems. Springer, Cham. https://doi.org/10.1007/978-3-319-16910-1_10

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  • DOI: https://doi.org/10.1007/978-3-319-16910-1_10

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-16909-5

  • Online ISBN: 978-3-319-16910-1

  • eBook Packages: EnergyEnergy (R0)

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