Course Details

Discrete Methods in Civil Engineering 2

DAB034 course is part of 24 study plans

Ph.D. full-t. program DPC-M compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. full-t. program DPC-K compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. full-t. program DPC-V compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. full-t. program DPC-E compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. full-t. program DPC-S compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. full-t. program DPC-GK compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. combi. program DKC-S compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. full-t. program DPA-S compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. combi. program DKC-V compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. full-t. program DPA-V compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. combi. program DKC-M compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. full-t. program DPA-M compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. combi. program DKC-K compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. full-t. program DPA-K compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. combi. program DKC-E compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. full-t. program DPA-E compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. combi. program DKC-GK compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. full-t. program DPA-GK compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. combi. program DKA-GK compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. combi. program DKA-S compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. combi. program DKA-M compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. combi. program DKA-K compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. combi. program DKA-V compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. combi. program DKA-E compulsory-elective Winter Semester 2nd year 10 credits

The discipline is devoted to description of processes via discrete equations. It consists of three parts: a) Stability of solutions. Stability of numerical algorithms. b) Application of difference equations. c) Control of processes using difference equations.

Course Guarantor

prof. RNDr. Josef Diblík, DrSc.

Institute

Institute of Mathematics and Descriptive Geometry

Learning outcomes

The purpose of continuation of this course is analysis of stability of linear and non-linear discrete systems and methods of their applications.

Prerequisites

The ability to orientate in the basic notions and problems
of discrete and difference equations.
Solving problems in the areas cited in the annotation.

Corequisites

Not required.

Planned educational 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.

Forms and criteria of assessment

A student will only receive credit if he will solve individual problems assigned by the teacher. The final examination will be only a written one lasting 90 minutes and consisting of 4 problems to calculate.

Objective

The purpose of continuation of this course is analysis of stability of linear and non-linear discrete systems and methods of their applications.

Specification of controlled instruction, the form of instruction, and the form of compensation of the absences

Vymezení kontrolované výuky a způsob jejího provádění stanoví každoročně aktualizovaná vyhláška garanta předmětu.

Lecture

3 hours/week, 13 weeks, elective

Syllabus of lectures

1. Stability of equilibrium points. Kinds of stabily and instability.
2. Stability of linear systems with the variable matrix.
3. Stability of nonlinear systems via linearization.
4. Ljapunov direct method of stability.
5. Phase analysis of two-dimensional linear discrete system with constant matrix, classification of equilibrium points.
6. Application of difference equations. Multiple-room heating problem. Newton law of cooling.
7. Discrete equivalents of continuous systems.
8. Discrete control theory.
9. The controllability and the complete controllability.
10. Matrix of controllability, the canonical forms of controllability, controllable canonical form, construction of the control algorithm.
11. Observability, complete observability, nononservability, principle of duality, the observability matrix, canonical forms of observability, relation of controllability and observability.
12.–13. Stabilization of control by feedback.