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DCL Lecture Series: Input-to-state stability of distributed parameter systems by Dr. Andrii Mironchenko

Event Type
Seminar/Symposium
Sponsor
Decision and Control Laboratory, Coordinated Science Laboratory
Location
CSL Auditorium
Date
Sep 25, 2013   3:00 - 4:00 pm  
Speaker
Dr. Andrii Mironchenko, University of Wurzburg
Contact
Angie Ellis
E-Mail
amellis@illinois.edu
Phone
217/300-1910
Views
2280

Decision and Control Lecture Series

Decision and Control Laboratory, Coordinated Science Laboratory

Input-to-state stability of distributed parameter systems

Andrii Mironchenko

Postdoctoral Research Assistant, Institute of Mathematics

University of Würzburg 

 Wednesday, September 25, 2013    

3:00 p.m. to 4:00 p.m.

B02 CSL Auditorium

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Abstract

We develop tools for investigation of input-to-state stability (ISS) of distributed parameter systems, described by differential equations in Banach spaces. We start our discussion with the ISS theory for linear systems, which already shows interesting features, which arise in the infinite-dimensional world. Next we develop Lyapunov methods for proving of ISS of nonlinear infinite-dimensional systems via Lyapunov methods. We generalize the small-gain theorem, known for interconnections of ODE systems, to the infinite-dimensional setting and apply it for construction of Lyapunov functions for interconnected system, on the basis of information about Lyapunov functions of subsystems.

Biography

Andrii Mironchenko recieved his M.Sc. degree in applied mathematics at I.I. Mechnikov Odessa National University in 2008 and his Ph.D. degree in mathematics at University of Bremen in 2012.  In 2012 he joined the Institute of Mathematics at the University of Würzburg as a research assistant (Postdoc).  His research interests include stability theory, distributed parameter systems, and applications of control theory to biological systems.

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