TTK4225 - Systems Theory, Introduction


Examination arrangement

Examination arrangement: Written examination
Grade: Letters

Evaluation form Weighting Duration Examination aids Grade deviation
Written examination 100/100 4 hours C

Course content

Fundamentals of complex algebra. The Laplace transform, applied to signals and linear systems. The inverse transformation. Properties. Impulse response and convolution. Transfer functions. Block diagrams and manipulation rules. "s" as a differentiation operator. Frequency response and spectrum. Fourier series and transforms of signals for linear systems. Convergence and existence of Fourier and Laplace transforms. Fourier as special case of Laplace. Fundamentals of linear algebra: Equation systems, linear transformations and eigenvalues. State space models with vector differential equations: Transition matrix, decoupling, similarity transformation. Relation to Laplace: resolvent matrix and transfer matrix. Linearization of nonlinear systems. Numerical solution of vector differential equations. Briefly about analog filters.

Learning outcome

Knowledge: Basic knowledge about mathematical tools for describing and analysing linear time-continuous signals and dynamic systems described by time responses and differential equations. Basic knowledge about models of systems in the form of n-dimensional differential equations. Knowledge of concepts like vector differential equations, state space model, eigenvalues. Knowledge of concepts like impulse- and step response,poles and zeros, block diagram and feedback.

Basic knowledge about modeling and analysis of continuous dynamical systems with transfer functions and frequency analysis, and representation of signals in the frequency domain. Knowledge about the Laplace- and Fourier transformations, and their connections, applied to signals and systems. Knowledge about the connections between state space models and transfer function models, and the equivalences between signals and linear systems. Knowledge about the most important types of signals and their spectral (frequency domain) representation. Knowledge about stability in linear systems.

Skills: Be able independently to model, and analyse signals' and dynamical systems' properties algebraically, and also numerically with MATLAB. - To find system time responses using the Laplace transform, via tables or residue calculus. - To do elementary analysis of signals and filter design in continuous time.

General competence: Be able to think about and apply the concepts of systems theory when considering technical and also non-technical systems. Be conscious about how this theory may contribute when cooperating with other disciplines.

Learning methods and activities

Lectures, computer exercises and calculation exercises. Compulsory computer exercises, using MATLAB.

Compulsory assignments

  • Excersises

Further on evaluation

Grades based 100% on the final written exam.
If there is a re-sit examination the examination form may change from written to oral.

Specific conditions

Exam registration requires that class registration is approved in the same semester. Compulsory activities from previous semester may be approved by the department.

Required previous knowledge

Mathematics corresponding to B.Sc. in engineering.

Course materials

Texbook and lecture notes, announced on its learning before start of semester.

Credit reductions

Course code Reduction From To
TTK4105 7.5 01.09.2019
More on the course



Version: 1
Credits:  7.5 SP
Study level: Second degree level


Term no.: 1
Teaching semester:  AUTUMN 2020

No.of lecture hours: 4
Lab hours: 4
No.of specialization hours: 4

Language of instruction: Norwegian

Location: Trondheim

Subject area(s)
  • Engineering Cybernetics
  • Technological subjects
Contact information
Course coordinator:

Department with academic responsibility
Department of Engineering Cybernetics



Examination arrangement: Written examination

Term Status code Evaluation form Weighting Examination aids Date Time Digital exam Room *
Autumn ORD Written examination 100/100 C
Room Building Number of candidates
  • * The location (room) for a written examination is published 3 days before examination date. If more than one room is listed, you will find your room at Studentweb.

For more information regarding registration for examination and examination procedures, see "Innsida - Exams"

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