Course Details

Discrete Methods in Civil Engineering II

Academic Year 2023/24

DA59 course is part of 12 study plans

​ D-P-C-SI (N) / PST Winter Semester 2nd year

​ D-P-C-SI (N) / FMI Winter Semester 2nd year

​ D-P-C-SI (N) / KDS Winter Semester 2nd year

​ D-P-C-SI (N) / MGS Winter Semester 2nd year

​ D-P-C-SI (N) / VHS Winter Semester 2nd year

​ D-K-C-SI (N) / VHS Winter Semester 2nd year

​ D-K-C-SI (N) / MGS Winter Semester 2nd year

​ D-K-C-SI (N) / PST Winter Semester 2nd year

​ D-K-C-SI (N) / FMI Winter Semester 2nd year

​ D-K-C-SI (N) / KDS Winter Semester 2nd year

​ D-K-C-GK / GAK Winter Semester 2nd year

​ D-K-E-SI (N) / PST 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.

Credits

10 credits

Language of instruction

Czech

Semester

winter

Course Guarantor

prof. RNDr. Josef Diblík, DrSc.

Institute

Institute of Mathematics and Descriptive Geometry

Forms and criteria of assessment

examination

Entry Knowledge

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

Aims

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

Basic Literature

J. Diblík. Diskrétní metody ve stavebnictví I, studijní materiál, 82 stran (cs)
J. Diblík. Diskrétní metody ve stavebnictví II, studijní materiál, 66 stran (en)
Saber, Elaydi, N. An Introduction to Difference Equations. Springer-Verlag 2010 (en)
Michael A. Radin. Difference Equations For Scientists And Engineering: Interdisciplinary Difference Equations, ‎ World Scientific, 2019 (en)

Recommended Reading

Farlow, S.J. An Introduction to Differential Equations, Dover Publications, 2006 (en)
Lakshmikantham, V., Trigiante, Donato. Theory of Difference Equations, Numerical Methods and Applications, Second Edition, Marcel Dekker, 2002 (en)

Syllabus

a)Stability of equilibrium points. Kinds of stabily and instability.
b)Stability of linear systems with the variable matrix.
c)Stability of nonlinear systems via linearization.
d)Ljapunov direct method of stability.
e)Phase analysis of two-dimensional linear discrete system with constant matrix, classification of equilibrium points.
f) Application of difference equations
g)Discrete equivalents of continuous systems.
h)Discrete control theory.
i)The controllability and the complete controllability.
j)Matrix of controllability, the canonical forms of controllability, controllable canonical form, construction of the control algorithm. k)Observability, complete observability, nononservability, principle of duality, the observability matrix, canonical forms of observability, relation of controllability and observability.
l)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.

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

https://www.vut.cz/en/students/courses/detail/272120

Lecture

13 weeks, 3 hours/week, elective

Syllabus

a)Stability of equilibrium points. Kinds of stabily and instability.
b)Stability of linear systems with the variable matrix.
c)Stability of nonlinear systems via linearization.
d)Ljapunov direct method of stability.
e)Phase analysis of two-dimensional linear discrete system with constant matrix, classification of equilibrium points.
f) Application of difference equations
g)Discrete equivalents of continuous systems.
h)Discrete control theory.
i)The controllability and the complete controllability.
j)Matrix of controllability, the canonical forms of controllability, controllable canonical form, construction of the control algorithm. k)Observability, complete observability, nononservability, principle of duality, the observability matrix, canonical forms of observability, relation of controllability and observability.
l)Stabilization of control by feedback.