Course detail
Algebraic Theory of Control
FSI-VTRAcad. year: 2024/2025
The students will be provided with the principles of the algebraic theory of discrete linear control. The basic algebraic concepts and methods used in the theory will be discussed. The main interest will be focused on the study of polynomials, because they are the
most important tools of the theory of discrete linear control. First, the fundamentals of the theory of rings and the theory of formal series will be expounded. This will be followed by the study of polynomials (as special cases of formal series) and polynomial matrices from the view-point of the theory of discrete linear control. This will be done with the help of the fundamental knowledge of the theory of rings.
Language of instruction
Number of ECTS credits
Mode of study
Guarantor
Department
Entry knowledge
Rules for evaluation and completion of the course
Since the attendance at lectures is not compulsory, it will not be checked, and compensation of possible absence will not be required.
Aims
Students will be made familiar with solving mathematical problems that occur in the theory of discrete linear control. Basic problems of this kind concern the synthesis of optimal control, which is reduced to searching for solutions of linear polynomial equations (as the transmission of a system can be expressed by using polynomials).
Study aids
Prerequisites and corequisites
Basic literature
Kučera V.: Discrete Linear Control: The Polynomial Equation Approach. Wiley, Chichester 1979. (EN)
V. Kučera: Algebraic Theory of Discrete-Time Linear Control. Academia, Praha 1978. (EN)
Recommended reading
J.Karásek, J.Šlapal: Teorie okruhů pro diskrétní lineární řízení, FSI VUT v Brně, 2000 (učební text) (CS)
Paul M. Cohn, Introduction to Ring Theory, Springer Undergraduate Mathematics Series, 2000, pp. 229 (EN)
V.Kučera: Algebraická teorie diskrétního lineárního řízení, Academia, Praha, 1978 (CS)
Elearning
Classification of course in study plans
Type of course unit
Lecture
Teacher / Lecturer
Syllabus
2.-3. Rings
4.-5. Fields
6.-7. Formal power series
8.-9. Polynomials
10.-11. Polynomial fractions
12.-13. Polynomial matrices
Elearning