Some selected contributions

Design of controllers

Control of uncertain systems via Lyapunov Redesign and Sliding Mode Control: Some results at the joint of both Lyapunov Redesign and SMC approaches for stabilization of some classes of uncertain time-delay systems are presented in Gomez, Ancona, Fridman, 2021,  Gomez, Ancona, Fridman, 2022. 

Safety control: In the last two years, I've been working on some results (under revision) with my colleague C. Diego Cruz-Ancona in a proposal of a new class of sliding manifolds that allows designing robust controllers that guarantee safety of the system trajectories. You can see a prelimnary of our ideas at this preprint 

Stability conditions: 

Necessary and sufficient condition of stability based on the delay Lyapunov matrix: The results obtained within my Ph.D thesis, published in Gomez, Egorov and Mondié, 2019 and Gomez, Egorov and Mondié, 2020 show that the stability of time-delay systems can be verified by checking the positive definiteness of a matrix depending on the delay Lyapunov matrix. An overview of the topic can be found in Mondié, Egorov, Gomez, 2022. An intriguing aspect that consistently motivated me throughout my Ph.D. journey was the fact that the matrix possesses finite dimension, despite time-delay systems being infinite-dimensional (kind of Borgian-like story)

Study of the H2 norm 

Study of the H2 norm of Differential Difference Algebraic Equations (DDAE): The H2 norm is an important performance measure in control theory. For DDAE, the H2 norm might be infinite even if there is not a direct feedtrhoguth term, and it might become infinite as a result of infinitesimal changes of the delays. The papers Gomez and Michiels, 2019, Gomez, Jungers and Michiels, 2020, and Gomez, Jungers and Michiels, 2020 address the problem of determining conditions for which the H2 norm for this class of systems is finite, and how one can compute it. An exciting moment in this research was when we realized that the so-called m-dimensional Cayley Hamilton Theorem gave the answer to the problem.