Input to state stability of distributed parameter systems. Habilitation Colloquium of Mironchenko A.
Talk at the Habilitation Colloquium of Andrii Mironchenko, University of Passau, Germany.
Title:
Input-to-state stability of distributed parameter systems
Speaker: Andrii Mironchenko, http://www.mironchenko.com/
00:12 Motivation
04:05 Main aim
04:55 Control systems
07:23 ISS
11:09 Vision of the field
12:38 Characterizations of ISS
17:53 ISS Lyapunov theorems
26:25 Small-gain theorems
30:19 Take-out message I: Toolbox for ISS
33:04 Semilinear evolution equations: Setting
34:42 Linear systems - well-posedness and stability
39:17 Non-coercive ISS Lyapunov theorems for linear systems
40:32 Semilinear evolution equations: Well-posedness
42:30 Linear methods help nonlinear theory
45:20 Summary
46:29 Open problems
The talk is based on the habilitation thesis "Input-to-state stability of distributed parameter systems", see:
http://mironchenko.com/__My_php_sourc...
and (partially) on a survey
A. Mironchenko, Ch. Prieur. "Input-to-State Stability of Infinite-Dimensional Systems: Recent Results and Open Questions"
https://epubs.siam.org/doi/abs/10.113...
Slides:
http://mironchenko.com/__My_php_sourc...
Abstract:
Input-to-state stability (ISS) allows estimating the impact of inputs and
initial conditions on both the intermediate values and the asymptotic bound on the solutions.
ISS has unified the input-output and Lyapunov stability theories and is a
crucial property in the stability theory of control systems as well as
for many applications whose dynamics depend on parameters, unknown perturbations, or other inputs.
In this talk, we sketch a broad picture of infinite-dimensional
input-to-state stability theory and discuss such key results as:
ISS superposition theorems, Lyapunov theory, stability analysis of networks,
as well as admissibility theory for linear systems.