Kies de Nederlandse taal
Course module: 191561560
Systems and Control
Course info
Course module191561560
Credits (ECTS)6
Course typeCourse
Language of instructionEnglish
Contact persondr. J.W. Polderman
dr. J.W. Polderman
Contactperson for the course
dr. J.W. Polderman
Academic year2016
Starting block
RemarksThis course is part of the Mastermath programme.
Application procedureYou apply via OSIRIS Student
Registration using OSIRISYes
Learning goals
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.
  • Control. By choosing inputs or, more general, by imposing additional constraints of the system may be influenced so as to obtain certain desired behavior.
The aim of the course is to become familiar with the basic concepts and more advanced notions of the mathematical theory of systems and control.

Learning Goals
After completion of the course the student is able to:
  1. Work with dynamical systems in which no distinction between input and outputs is made and to work with system theoretic notions in terms of such models. In particular to obtain full row rank or minimal representations.
  2. Classify equivalent model descriptions through algebraic manipulations
  3. Analyze dynamical systems in input/output and input/state/output form
  4. To understand and analyze controllability and observability of dynamical systems
  5. Derive a manifest model description from a model with latent variables
  6. To analyze stability properties and to synthesize a stabilizing controller through pole placement.
  7. To synthesize observers in combination with controller design.
  8. Present a topic from the literature in oral and written form.
Notice: National course - Mastermath Utrecht

Course description
Linear time-invariant differential systems, algebraic representation of dynamical systems using polynomial matrices. Minimal representations. Autonomous systems. State space models and the Markov property. Nonlinear systems and linearization. Controllability and observability. Latent variable models. Stability of state space models. Stabilization by state feedback and by dynamic feedback. Basic observer theory and its relation to filter theory. Transfer matrices and the connection with state space models and behaviors. Poles of transfer matrices and the connections with internal stability and input-output stability. Injective and surjective dynamic systems and the connection to invertibility. Zeros of transfer matrices and the connection to invertibility of dynamic systems. Relationship with tracking problems. Zero-dynamics and minimum-phase systems. Connections with unstable pole-zero cancellation and the problems of infinite zeros.

This course is part of the MasterMath program. Information about the course (description, organization, examination and prerequisites) can be found on

The UT contact person for this course is J.W. Polderman.

Assumed previous knowledge
Calculus and Linear Algebra
Required materials
Introduction to Mathematical Systems theory: a Behavioral Approach, by J.W. Polderman and J.C. Willems (Springer, New York, 1998).
Recommended materials
Instructional modes

Homework, presentation and exam

Homework, oral and written presentation, and written exam

Kies de Nederlandse taal