Systems Theory


Upon conclusion the student will be able to analyse the dynamic behaviour of systems in his area of expertise, and to design and tune control systems of small complexity.The course aims to develop the initiative, critical mind, autonomy and implementation abilities.


General characterization





Responsible teacher

Fernando José Almeida Vieira do Coito


Weekly - 5

Total - 64

Teaching language




- integral and differential calculus; differential equations

-complex numbers; complex functions


- forces and movement; Newton''''s Laws



  • Katsyhiko Ogata, System Dynamics, Prentice-Hall
  • B. J. Kuo, Automatic Control Systems, Prentice-Hall
  • Katsyhiko Ogata, Modern Control Engineering, Prentice-Hall
  • Franklin;-- Powell;-- Emami-Naeini, Feedback Control of Dynamic Systems, Addison-Wesley
  • Texts for all the chapters  (in portuguese)


  • ernando Coito, Lessons on System Theory (in portuguese) 

Teaching method

Theoretical class: exposition of theoretical concepts; applicatioon examples.

Practical and laboratorial classes: propblem resolution, realization of practical works to understand the concepts; realization of short projects.

Evaluation method

Thr approval in the Systems Theory course can be obtained in one of two alternative ways:

1. An average of 9.5 points or above (scale 0-20 points) on 2 evaluation tests to be performed during the semester (with a weight of 50% each).

2. A minimum grade of 9.5 on a final exam. The grade obtained in the exam will be the final grade of the course.

Both tests and exam will have two evaluation components: a theoretical/practical component and a laboratory component. The evaluation of the laboratory component will be based on the work proposed for the laboratory classes. This component corresponds to 25% of the evaluation (5 points).

Attendance of laboratory practical classes is not compulsory. At the end of each practical class a questionnaire will be conducted on the activity performed in the class. Students who answer the questionnaires in class are exempted from performing the laboratory component of the corresponding tests, as well as the exam.

Students who have scored on this component in previous school years are not required totake the quizzes. In this case the classification of the laboratory component will be calculated from the practical classification obtained previously, converted to the range of 0 to 5 points.

For consultation purposes during the tests and exam, the students may take with them one A4 sheet. The information included on the A4 sheet may consist on any subject the student considers useful, such as formulas, tables or information about laboratory work. The use of calculators is allowed. Mobile phones will not be allowed.

Subject matter

1. Introducing dynamic systems:

1.1. Introduction

1.2. Relevant test signals

1.3. System properties (linearity, time invariance, causality)

1.4. Dynamic systems 1.5 Introduction to the discrete-time signals and systems.

2. Mathematics:

2.1. Complex numbers 2.2. Laplace transform

3. Time analysis:

3.1. First order systems 3.2. Second order systems 3.3. Higher order systems

4. Control systems in the time domain:

4.1. Feedback 4.2. Set-point tracking 4.3. Stability. 4.4. PID controllers

5. Control systems in the frequency domain:

5.1. Frequency behavior 5.2. Bode diagrams 5.3. The relationship between time and frequency  5.4. Control system specifications 5.4. Nyquist criterion 5.5. Gain and phase margins


Programs where the course is taught: