Federico Milano received from the University of Genoa, Italy, the ME and Ph.D. in Electrical Eng. in 1999 and 2003, respectively. From 2001 to 2002 he was with the University of Waterloo, Canada, as a Visiting Scholar. From 2003 to 2013, he was with the University of Castilla-La Mancha, Spain. In 2013, he joined the Univ. College Dublin, Ireland, where he is currently Professor of Power Systems Control and Protections and Head of Electrical Engineering. His research interests include power system modelling, control and stability analysis. A Fellow of the IEEE and the IET, he has been an editor for several journals published by IEEE, IET, Elsevier and Springer, including the IEEE Transactions on Power Systems and IET Generation, Transmission & Distribution. He has authored or co-authored about 150 peer reviewed journal and conference papers, several book chapters and three books (published by Springer, McGraw Hill and Cambridge University Press) and edited one book (published by IET).

Ioannis Dassios is currently a UCD Research Fellow at AMPSAS, University College Dublin, Ireland. He studied Mathematics and completed a two-year MSc in Applied Mathematics & Numerical Analysis at the Department of Mathematics, University of Athens, Greece with grade "Excellent" (highest mark in the Greek system). As a MSc student he received a travel grant to visit the Department of Mathematics at the University of North Texas, USA. In July 2013 he received his PhD in Mathematics from the Department of Mathematics, University of Athens, Greece, focusing on singular discrete dynamical systems and their applications. Since then, he has been a Post-Doctoral Researcher at MACSI (Mathematics Applications Consortium for Science and Industry), Department of Mathematics & Statistics, University of Limerick, Ireland and a Senior researcher at ERC/ESIPP, University College Dublin, Ireland. Previously, he worked as a Post-Doctoral Research & Teaching Fellow at the School of Mathematics, University of Edinburgh, UK, and for six months as a Post-Doctoral Research Associate at the Modelling and Simulation Centre, University of Manchester, UK. He has published 45 articles (16 single authored, and 29 co-authored with researchers from Universities and Industries) in internationally leading academic journals. He is an Editor in Applied Sciences, Signals, and has also served as a reviewer 333 times in 66 different journals.

Muyang Liu received from University College Dublin, Ireland, the ME in Electrical Energy Engineering in 2016. Since September 2016, she is a Ph.D. student candidate with University College Dublin. Her scholarship is funded through the SFI Investigator Award with title "Advanced Modelling for Power System Analysis and Simulation". Her current research interests include small-signal and transient stability analysis of power systems modelled through functional differential-algebraic equations.

Georgios Tzounas received from National Technical University of Athens, Greece, the ME in Electrical and Computer Engineering in 2017. Since September 2017, he is Ph.D. candidate with University College Dublin. His scholarship is funded through the SFI Investigator Award with title "Advanced Modelling for Power System Analysis and Simulation." His current research interests include eigenvalue problems as well as stability analysis and robust control of power system with inclusion of measurement delays.

Part I Introduction

1. Power Systems Outlines

2. Mathematical Outlines

Part II Linear Eigenvalue Problema

3. Di¿erential Equations with Regular Pencil

4. Explicit Di¿erential-Algebraic Equations

5. Implicit Di¿erential-Algebraic Equations

6. Di¿erential Equations with Singular Pencil

7. Mobius Transform

8. Participation Factors

Part III Non-Linear Eigenvalue Problems

9. Polynomial Eigenvalue Problem

10. Delay Di¿erential Equations

11. Systems with Constant Delays

12. Systems with Time-Varying Delays

Part IV Numerical Methods

13. Numerical Methods for Eigenvalue Problems

14. Open Source Libraries

15. Large Eigenvalue Problems

V Appendices