Course detail

Robust and algebraic control

FEKT-MRALAcad. year: 2015/2016

The course is focused on application of algebraic theory for control circuit’s synthesis. It consists of algebraic theory, the controller designs using polynomial methods, structured and unstructured uncertainties of dynamic systems and introduction into robust control.

Learning outcomes of the course unit

The student are able to use algebraic methodes of controller design and they know how to design robust controller.


The subject knowledge on the Bachelor´s degree level is requested.


Not applicable.

Recommended optional programme components

Not applicable.

Recommended or required reading

Kučera:Algebraická teorie reg.,Academia Press (CS)
Štecha, Havlena: Moderní teorie řízení, ČVUT Praha (CS)
Doyle, Francis, Tannenbaum: Feedback Control Theory, Macmillan Publishing (EN)
Scherer, Weiland: Linear matrix inequalities in control. DISC, 2000 (EN)

Planned learning activities and teaching methods

Teaching methods depend on the type of course unit as specified in the article 7 of BUT Rules for Studies and Examinations. Materials for lectures and exercises are available for students from web pages of the course. Students have to write a single project/assignment during the course.

Assesment methods and criteria linked to learning outcomes

Exercises. Individual project. Max. 30 points.
Written exam. Max 70 points.

Language of instruction


Work placements

Not applicable.

Course curriculum

1. Introduction into problematic.
2. Algebraic theory. Solution of polynomial equation, general solution, special solutions, solvability condition.
3. Application of algebraic methods to simple controller designs. Pole placement method, exact model matching problem, the group of stabilizing controllers.
4. Sensitivity function shaping design. Sensitivity function and modulus margin, sensitivity function template, additional polynomials in controller and in its design.
5. Time optimal discrete control. Feedforward control,
6. Quadraticaly optimal discrete control, 1DOF, 2DOF, finite and stable time optimum control with nonzero initial conditions.
7. Stochastic control. Minimum variance control, the evaluation of MVC controllers, generalized minimum variance control.
8. Interval polynomials. Zero exclusion principle, value sets, Mikhailov-Leonard stability criteria, Kharitonov polynomials.
9. Inroduction into robust control. The notion of robustness, norms of the system and signal, LFT, system matrices and their operations.
10. Description of uncertainties. Parametric and nonparametric uncertainties, their description in Matlab Simulink.
11. Mixed sensitivity design, GS controller. Similarities with sensitivity function shaping method.
12. Course summary


To introduce to the students universal tool for solving tasks of automatic control and to became familiar with robust control. and CASE systems.

Specification of controlled education, way of implementation and compensation for absences

The content and forms of instruction in the evaluated course are specified by a regulation issued by the lecturer responsible for the course and updated for every academic year.

Classification of course in study plans

  • Programme EEKR-M1 Master's

    branch M1-KAM , 1. year of study, summer semester, 5 credits, optional specialized

  • Programme EEKR-M Master's

    branch M-KAM , 2. year of study, summer semester, 5 credits, optional specialized

  • Programme EEKR-CZV lifelong learning

    branch ET-CZV , 1. year of study, summer semester, 5 credits, optional specialized

Type of course unit



26 hours, optionally

Teacher / Lecturer

Fundamentals seminar

14 hours, compulsory

Teacher / Lecturer

Exercise in computer lab

12 hours, compulsory

Teacher / Lecturer