Mironchenko. Revisiting Lyapunov-Krasovskii method for robust stability analysis of delay systems.

Talk at the Online Seminar on Input-to-State Stability and its Applications

Title: Revisiting Lyapunov-Krasovskii methodology for robust stability analysis of time-delay systems

Slides:

00:17 Time-delay systems
02:57 UGAS and ISS
05:52 ISS Lyapunov-Krasovskii functional with norm-dissipation
09:49 Chaillet Conjecture
14:32 V-stability
19:15 Take-home Slide I: ISS Superposition Theorems
20:39 Lyapunov conditions for V-UGS
21:40 V-ISS Lyapunov-Krasovskii’s theorem
30:50 Comparison to known results
32:16 Take Home Slide II: LK theorem with pointwise dissipation
34:50 Strengthening Krasovskii’s theorem
36:14 Outlook

Abstract:
Lyapunov-Krasovskii functionals are a classical tool to study asymptotic stability
and input-to-state stability (ISS) of time-delay systems. However, in the ISS context,
the requirements on the Lyapunov-Krasovskii functionals are much stronger than those used for analysis of asymptotic stability.
In this talk, we show a Lyapunov-Krasovskii theorem for ISS of time-delay systems.
This theorem is valid for systems with mild regularity of the right-hand side and
imposes fewer requirements on the Lyapunov-Krasovskii functional than the known results.
Finally, we derive a stronger property than classical ISS. To prove this result,
we introduce a new stability formalism for delay systems with inputs and establish
the ISS superposition theorem specifically tailored for time-delay systems.

Biography:
Andrii Mironchenko was born in 1986 in Odesa, Ukraine. He received a Ph.D. degree in mathematics
from the University of Bremen, Germany, and a habilitation degree from the University of Passau, Germany.
He was a Postdoctoral Fellow of the Japan Society for Promotion of Science (2013–2014).
Since 2023, he has been with the Department of Mathematics, University of Klagenfurt, Austria.
Dr. Mironchenko is the author of the monograph „Input-to-State Stability“ (Springer, 2023)
and of 70 journal and conference papers on control theory and applied mathematics.
A. Mironchenko is an Associate Editor in Systems & Control Letters and
is a co-founder and co-organizer of the biennial Workshop series
“Stability and Control of Infinite-Dimensional Systems” (SCINDIS, 2016 - now).
He is a Senior Member of IEEE. He is a recipient of 2023 IEEE CSS George S. Axelby Outstanding Paper Award.
His research interests include stability theory, nonlinear systems theory, distributed parameter systems,
hybrid systems, and applications of control theory to biological systems and distributed control.

Date:

Wednesday, 17th January 2024