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Achim Ilchmann


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Ihre Position


10th Elgersburg School 2018 (March 4 - March 10, 2018)

Vladimir L. Kharitonov (Saint-Petersburg): Time-delay systems: Lyapunov functionals and matrices
Sergey Dashkovskiy (Würzburg): Input-to-state stability and interconnected Systems

The school is on two topics of current interest in the field of systems and control theory and its applications. Each topic is presented by a leading expert in the field. In addition to the lectures there will be example classes. Participants will attend both courses.
For more information about the current courses click on "Courses".

Who can attend?
The school is open to international PhD and advanced undergraduate students from engineering sciences or mathematics. A background in systems and control theory or related fields will be required.

A limited number of scholarships will be available. These scholarships will in general cover the full travel and lodging expenses. Because of the restricted number of such scholarships, we ask that students preferentially use funds available at their home institutions.

Participants will attend both courses.

Arrival:      Sunday,  March 4, 2018
Departure: Saturday, March 10, 2018


Deadline for applications:  
Please make sure that Achim Ilchmann receives a CV from the applicant and
a  short letter of recommondation from the supervisor, both by email.


The workshop takes place in the Hotel "Am Wald" in Elgersburg (Thuringia).

The cost for the hotel including full board (including Sunday evening March 4 and

Saturday morning March 10) is EUR 520,- for a single room and EUR 420,- for a double room per person.

The costs will be covered for participants receiving scholarships.

More detailed information about the hotel and about Elgersburg can be found at the following web pages:

"Hotel am Wald" Elgersburg



Introduction to ISS with application to interconnected Systems

Prof. Dr. Sergey Dashkovskiy
University of Würzburg

Introduction to ISS with application to  interconnected systems

Stability is one of the fundamental properties of dynamical systems.
In case of nonlinear systems subject to external signals characterization
of stability properties becomes essentially more complex then in case 
of linear ones.
One suitable notion in this case is the input-to-state stability.
Together with aligned stability notions there is a framework 
comprising several possibilities
to describe the influence of the input signal on an equilibrium of the system.
It turns out that this framework is particularly useful to study 
stability of interconnected system.

After an introduction to the framework of input-to-state stability and 
related notions as well as
different characterizations of these properties we will consider their 
applications to interconnected systems.
In particular the small-gain theory including contructions of 
ISS-Lyapunov functions will be given
and illustrated by a number of examples.

Time-delay systems: Lyapunov functionals and Matrices

Prof. Dr. Vladimir Kharitonov
Saint-Petersburg State University

Time-delay systems: Lyapunov functions and matrices

In this course we consider the class of retarded type linear systems with one delay. We introduce the fundamental matrix of such a system, and provide an explicit expression for the solution of an initial value problem. Exponential stability conditions both in terms of characteristic eigenvalues of the system, and in terms of Lyapunov functions are presented. The general scheme for the computation of quadratic funcitons with prescribed time derivaties alog the sotuions of the time-delay system is explained in detial. it is demonstrated that theses functionals are defined by special Lypunov matrices. The matirices are natural counterpart of the classical Lyapunov matrices that appear in the computation of Lypunov quadratic forms for a deya free linear systems. A substantial part of the course is devoted to analysis of basic properties of the Lyapunov matrices. Then, Lyapunov complete type functionals that admit various quadratic lower and upper bounds are introduced. Finally, we make use of the complete type functionals in order to derive exponential estimates of the solutions of time-dely systems, robustness bounds for pertubed systems, evalution of quadratic performance indices.


08:30Kharitonov: DelayDashkovsky: ISSKharitonov: DelayDashkovsky: ISSKharitonov: Delay
10:00Coffee & Tea
10:30Dashkovsky: ISSKharitonov: DelayDashkovsky: ISSKharitonov: DelayDashkovsky: ISS
14:30Work on
ex. sheet Delay
Work on
ex. sheet ISS
ExcursionWork on
ex. sheet ISS
Work on
ex. sheet Delay
ex. sheet Delay
ex. sheet ISS
ex. sheet ISS
ex. sheet Delay
16:45Coffee & TeaCoffee & Tea
17:15Work on
ex. sheet ISS

Work on
ex. sheet Delay 

Work on
ex. sheet Delay
Work on
ex. sheet ISS
ex. sheet ISS
ex. sheet Delay

ex. sheet Delay

ex. sheet ISS


Achim IlchmannTU Ilmenau
Timo ReisU Hamburg
Fabian WirthU Passau


  • Vladimir Kharitonov
    Saint-Petersburg State University

  • Sergey Dashkovskiy
    University of Würzburg


  • Alexey Egorov
    KU Leuven

  • Petro Feketa
    TU Kaiserslautern


Achim Ilchmann 
  (TU Ilmenau)

Timo Reis
  (U Hamburg)

Fabian Wirth
  (Universität Passau)


Herewith I register for the 10th Elgersburg School.
(arrival: March 4th in the evening;  departure: March 10 in the morning)

The cost for the hotel including full board is
EUR 520,- for a single and EUR 420,- for a double room.

Confirmation notice
The number of participants is strictly limited to 40 due to the size of the workshop hotel. If more than 40 registrations are received, the organizers will rank registrations according to expertise in systems and control and invite the first 40 of this list. Confirmation notices will be sent out before Dec. 15, 2017.

  • A CV of the applicant is required and an e-mail of the supervisor is required including
  • Recommendation of the applicant for the summer school.
  • Declaration whether the applicant needs financial support.
  • A statement whether the applicant would be able to come if no financial support can be provided.

Please send this e-mail to Achim Ilchmann


Elgersburg can be reached via local trains from Erfurt, which is connected to the German high speed train network.

Trains from Erfurt to Elgersburg (destination Ilmenau) run every hour.

The nearest airport is Leipzig, which has few international connections.

From the major airports in Frankfurt and Berlin, Erfurt can be reached by train in 2-3 hours.

Frankfurt has the advantage, that there are direct trains between the airport and Erfurt.