Course Details

# Discrete Methods in Civil Engineering 2

DAB034 course is part of 23 study plans

DPC-S Winter Semester 2nd year

DPC-M Winter Semester 2nd year

DPC-K Winter Semester 2nd year

DPC-GK Winter Semester 2nd year

DPC-E Winter Semester 2nd year

DPA-V Winter Semester 2nd year

DPA-S Winter Semester 2nd year

DPA-M Winter Semester 2nd year

DPA-K Winter Semester 2nd year

DPA-GK Winter Semester 2nd year

DPA-E Winter Semester 2nd year

DKC-V Winter Semester 2nd year

DKC-S Winter Semester 2nd year

DKC-M Winter Semester 2nd year

DKC-K Winter Semester 2nd year

DKC-GK Winter Semester 2nd year

DKC-E Winter Semester 2nd year

DKA-V Winter Semester 2nd year

DKA-S Winter Semester 2nd year

DKA-M Winter Semester 2nd year

DKA-K Winter Semester 2nd year

DKA-GK Winter Semester 2nd year

DKA-E Winter Semester 2nd year

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

Institute

Objective

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

Syllabus

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.

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.

Language of instruction

Czech

Credits

10 credits

Semester

winter

Forms and criteria of assessment

examination

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

Extent and forms are specified by guarantor’s regulation updated for every academic year.

Offered to foreign students

Not to offer

Course on BUT site

Lecture

13 weeks, 3 hours/week, elective

Syllabus

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.