Research

My research interests focus on pure and applied mathematics, and include

• Science communication and Effective Graphical Display.
• Data Science;
• Mathematical Modeling, Simulation and Computation;
• Uncertainty Quantification, Statistics, and Probability;
• Optimization, Control Theory, and Machine Learning;
• Approximation Theory, Integration Methods and Model Order Reduction;

PhD in Engineering Science

Department of Computer Science
NUMA research unit - Numerical Analysis and Applied Mathematics
KU Leuven, Leuven (Belgium)
February 2020

Title

Looking for stability
Advances on spectrum-based stability and stabilization of uncertain time delay system

Author

Luca Fenzi

Supervisor

Prof. Dr. Ir. Wim Michiels

Keywords

Linear time-delay systems (autonomous and periodic);
Dynamical systems stability and Control Theory;
Uncertain Quantification;
Eigenvalue problems;
Polynomial approximation.

PhD Thesis

View online (150 pages , English)

Poster

View online (1 page, English)

Presentation

1. L. Fenzi and W. Michiels
   Robust stability optimization for delay systems in a probabilistic framework
   Linear Algebra and its Applications, 526, 1-26 (2017).
   (Preprint) L. Fenzi and W. Michiels. Robust stability optimization for delay systems in a probabilistic framework Internal report TW671, Department of Computer Science, KU Leuven, August 2016.


2. L. Fenzi, D. Pilbauer, W. Michiels and T. Vyhlidal
   A probabilistic approach towards robust stability optimization, with application to vibration control
   Proceeding of ENOC 2017, Budapest, Hungary (2017).


3. L. Fenzi and W. Michiels
   Polynomial (chaos) approximation of maximum eigenvalue functions: efficiency and limitations
   Numerical Algorithms 82, 1143-1169 (2019).
   (Tutorial) L. Fenzi and W. Michiels. Experiments on polynomial (chaos) approximation of maximum eigenvalue functions: Tutorial, Technical report TW 688, Department of Computer Science, KU Leuven (2018).
   (Preprint) L. Fenzi and W. Michiels. Polynomial (chaos) approximation of maximum eigenvalue functions: efficiency and limitations, arXiv: 1804.03881 (2018).
   


4. W. Michiels and L. Fenzi
   Spectrum-based Stability Analysis and Stabilization of Time-periodic Time-delay Systems
   SIAM Journal on Matrix Analysis and Applications 41(3), 1284-1311 (2020).
   (Preprint) W. Michiels and L. Fenzi. Spectrum-based stability analysis and stabilization of a class of time-periodic time-delay systems arXiv: 1804.03881 (2019).
   


5. L. Fenzi
   Looking for Stability
   Advances on Spectrum-based Stability and Stabilization of Uncertain Time-Delay Systems
   PhD Thesis, KU Leuven (2020).
   

Conferences, Seminars and Workshops

1. Oral presentation: Esistenza del Trascendente, Dimostrazioni dell’esistenza di numeri e serie formali trascendenti. Rete di Idee, ISUFI Lecce (Italy), October 27, 2012.


2. Oral presentation: Pedestrian Flows, Un nuovo modello. Rete di Idee, Scuola Normale di Pisa and Sant'Anna, scuola universitaria superiore (Italy), October 23-25, 2015.


3. Attendance. Dynamical Systems, Control and Optimization (DYSCO) Study Day, Louvain-la-Neuve (Belgium), May 19, 2016.


4. Attendance. System Structure and Control (SSSC) 2016 & Time Delay Systems (TDS) 2016, Istanbul (Turkey), June 22-24, 2016.


5. Technical Assistant. International Linear Algebra Society (ILAS) Conference 2016, Leuven (Belgium), July 11-15, 2016.


6. Oral presentation: Robust stability optimization for delay differential algebraic equations in a probabilistic framework. European Conference on Computational Optimization (EUCCO), Leuven (Belgium), September 12-14, 2016.


7. Attendance. Summer School on Uncertainty Quantification, WIAS/GAMM/TUM Berlin (Germany), September 12-16, 2016.


8. Seminar: A probabilistic approach towards robust stability optimization, with applications. NUMA seminar at KU Leuven, Leuven (Belgium), May 11, 2017.


9. Oral presentation: A probabilistic approach towards robust stability optimization, with applications. Workshop on Computational aspects of Time Delay System theory with Applications at CTU, Prague (Czechia), May 18, 2017.


10. Seminar: A probabilistic approach towards robust stability optimization, with application to vibration control. European Nonlinear Dynamics Conference (ENOC) 2017, Budapest (Hungary), June 25-30, 2017.


11. Oral presentation: Polynomial (chaos) approximation of the spectral abscissa: efficiency and limitations. Time Delay Systems (TDS) 2018, Budapest (Hungary), June 28-30, 2018.


12. Seminar: LaTeX: Tips & Tricks SIAM student chapter KU Leuven Workshop, Leuven (Belgium), November 20, 2019.


13. Seminar: Periodic Time Delay Systems: stability and stabilization by spectrum-based approach. NUMA seminar at KU Leuven, Leuven (Belgium), May 9, 2019.


14. Attendance. Advanced Courses, Controlling Delayed Dynamics: Advances in Thoery Methods and Applications. , CISM Udine (Italy), November 25-29, 2019.


15. Oral Presentation: Alla ricerca della stabilità: migliorare la stabilità di sistemi dinamici con ritardo ottimizzando gli autovalori. 1° Ritrovo Matematico degli Alumni della Scuola Superiore dell'Università degli Studi di Udine, Udine (Italy), December 21, 2019.