Course Details

Discrete Methods in Civil Engineering II

DA59 course is part of 22 study plans

Ph.D. full-t. program nD > PST compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. full-t. program nD > FMI compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. full-t. program nD > KDS compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. full-t. program nD > MGS compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. full-t. program nD > VHS compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. combi. program nDK > PST compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. combi. program nDK > KDS compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. combi. program nDK > VHS compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. combi. program nDK > FMI compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. combi. program nDK > MGS compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. full-t. program nDA > PST compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. full-t. program nDA > FMI compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. full-t. program nDA > KDS compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. full-t. program nDA > MGS compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. full-t. program nDA > VHS compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. combi. program nDKA > PST compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. combi. program nDKA > FMI compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. combi. program nDKA > KDS compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. combi. program nDKA > MGS compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. combi. program nDKA > VHS compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. full-t. program I > GAK compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. combi. program IK > GAK 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.

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.

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

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.