COURSE ITB- UTwente collaboration Mathematical Theory of Systems and Control

Mathematical Theory of Systems and Control
2‐week COURSE ITB- UTwente collaboration
Period: 18-30 Januari 2009
Place: Campus ITB
Lecturers
From Applied Mathematics, UTwente
􀂾 Dr. J.W. Polderman
􀂾 Prof. A. Stoorvogel
From Electrical Engineering, ITB
􀂾 Dr. B. Riyanto (ITB)
􀂾 Dr. A. Syaichurochman

Fellowships for Combined MSc/PhD are available for excellent performers

Organization of the course
The course will consist of lectures and exercise classes with written
assignments.
In the second week, small groups will be formed to execute a more
challenging assignment slightly beyond the material covered in the
lectures; at the end of the second week each group will give a
presentation.
During the course, seminars, by the lecturers, as well as by
researchers from ITB, will be given to highlight more advanced current
research topics in the field of S&C.
The main reference for the course is:
Introduction to Mathematical Systems theory: a Behavioral Approach, by
J.W. Polderman and J.C. Willems (Springer, New York, 1998).

Overview of the topics of the course
Mathematical systems theory is concerned with problems related to
dynamic phenomena in interaction with their environment.
These problems include:
• Modeling. Obtaining a mathematical model that reflects the main
features. A mathematical model may be represented by difference or
differential equations, but also by inequalities, algebraic equations,
and logical constraints.
• Analysis and simulation of the mathematical model.
• Prediction and estimation. Identification of the system behavior
based on noisy and incomplete measurements.
• Control. By choosing inputs or, more general, by imposing additional
constraints on some of the variables, the system may be influenced so
as to obtain certain desired behavior. Feedback is an important
example of control.
The course provides an introduction to recent developments in the area
of Systems and Control, while at the same time covering the standard
theory. The main objects of study in the course are systems modeled by
linear time‐invariant differential equations. We start with a
treatment of the theory of algebraic representation of dynamical
systems using polynomial matrices. The main result is a complete
characterization of all representations of a given system.
Several other representations are introduced along with their
relations. Important examples of such representation are input‐output
representations that reveal that some variables are unrestricted by
the equations, and state space representations that visualize the
separation of past and future, also referred to as the Markov
property. Controllability and observability are important system
theoretic concepts. A controllable system has the property that a
desired future behavior can always be obtained, independent of the
past behavior, provided that this future behavior is compatible with
the laws of the system. Observability means that the complete behavior
may be reconstructed from incomplete observations. The theory of
controllability and observability forms one of the highlights of the
course.
Stability can be an important and desirable property of a system.
Stabilization by static or dynamic feedback is one of the key features
of Systems and Control. In the pole placement theorem linear algebraic
methods and the notion of controllability are used in their full
strength. The theorem, loosely speaking, says that in a controllable
system the dynamic behavior can be changed as desired, in terms of
characteristic values, by using appropriate feedback. It forms one of
the most elegant results of the course and indeed of the field of
Systems and Control.

Further information
Detailed information about the course content and organization is
available at:
www.math.utwente/~poldermanjw/ITBcourse

Application
A limited number of students form outside the study programme EE at
ITB can be accommodated to participate. Application is required and
can be done via an electronic webform available at
www.labmath‐indonesia.or.id. Please attach the required documents: CV,
letter of motivation, and proof of English proficiency.

MSc in Systems and Control
The course is compulsory in the curriculum of the Master Programme in
Systems and Control at the University of Twente. Information about the
MSc Programme in Systems and Control may be found at
http://sc.graduate.utwente.nl.
For excellent participants there is a limited number of fellowships to
enroll in this master programme as part of a combined Msc‐PhD track.

UT‐Info & Support Office in Bandung
General information about studying at the University of Twente can be
obtained from http://graduate.utwente.nl
Personal assistance in selecting a Master programme or to look for
possibilities for a PhD project can be obtained at the UT‐Info &
Support Office hosted at LabMath‐Indonesia
Jalan Anatomi 19, Bandung 40191
international@labmath‐indonesia.or.id