Course Details
Discrete Methods in Civil Engineering II
Academic Year 2022/23
DA59 course is part of 22 study plans
D-K-E-SI (N) Winter Semester 1st year
D-K-E-SI (N) Winter Semester 1st year
D-K-E-SI (N) Winter Semester 1st year
D-K-E-SI (N) Winter Semester 1st year
D-K-E-SI (N) Winter Semester 1st year
D-K-C-SI (N) Winter Semester 1st year
D-K-C-SI (N) Winter Semester 1st year
D-K-C-SI (N) Winter Semester 1st year
D-K-C-SI (N) Winter Semester 1st year
D-K-C-SI (N) Winter Semester 1st year
D-P-E-SI (N) Winter Semester 1st year
D-P-E-SI (N) Winter Semester 1st year
D-P-E-SI (N) Winter Semester 1st year
D-P-E-SI (N) Winter Semester 1st year
D-P-E-SI (N) Winter Semester 1st year
D-P-C-SI (N) Winter Semester 1st year
D-P-C-SI (N) Winter Semester 1st year
D-P-C-SI (N) Winter Semester 1st year
D-P-C-SI (N) Winter Semester 1st year
D-P-C-SI (N) Winter Semester 1st year
D-P-C-GK Winter Semester 1st year
D-K-C-GK Winter Semester 1st 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
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.
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
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.