Course detail
Discrete Methods in Civil Engineering 2
FAST-DAB034Acad. year: 2021/2022
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.
Language of instruction
Czech
Number of ECTS credits
10
Mode of study
Not applicable.
Guarantor
Department
Institute of Mathematics and Descriptive Geometry (MAT)
Learning outcomes of the course unit
Not applicable.
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.
of discrete and difference equations.
Solving problems in the areas cited in the annotation.
Co-requisites
Not applicable.
Planned learning activities and teaching methods
Not applicable.
Assesment methods and criteria linked to learning outcomes
Not applicable.
Course curriculum
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.
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.
Work placements
Not applicable.
Aims
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 education, way of implementation and compensation for absences
Extent and forms are specified by guarantor’s regulation updated for every academic year.
Recommended optional programme components
Not applicable.
Prerequisites and corequisites
Not applicable.
Basic literature
Not applicable.
Recommended reading
Not applicable.
Classification of course in study plans
- Programme DPA-M Doctoral 2 year of study, winter semester, compulsory-optional
- Programme DPC-M Doctoral 2 year of study, winter semester, compulsory-optional
- Programme DPA-K Doctoral 2 year of study, winter semester, compulsory-optional
- Programme DPC-K Doctoral 2 year of study, winter semester, compulsory-optional
- Programme DPA-V Doctoral 2 year of study, winter semester, compulsory-optional
- Programme DPC-V Doctoral 2 year of study, winter semester, compulsory-optional
- Programme DPA-S Doctoral 2 year of study, winter semester, compulsory-optional
- Programme DPC-S Doctoral 2 year of study, winter semester, compulsory-optional
- Programme DPA-E Doctoral 2 year of study, winter semester, compulsory-optional
- Programme DPC-E Doctoral 2 year of study, winter semester, compulsory-optional
- Programme DPA-GK Doctoral 2 year of study, winter semester, compulsory-optional
- Programme DPC-GK Doctoral 2 year of study, winter semester, compulsory-optional
- Programme DKA-M Doctoral 2 year of study, winter semester, compulsory-optional
- Programme DKC-M Doctoral 2 year of study, winter semester, compulsory-optional
- Programme DKA-K Doctoral 2 year of study, winter semester, compulsory-optional
- Programme DKC-K Doctoral 2 year of study, winter semester, compulsory-optional
- Programme DKA-V Doctoral 2 year of study, winter semester, compulsory-optional
- Programme DKC-V Doctoral 2 year of study, winter semester, compulsory-optional
- Programme DKA-S Doctoral 2 year of study, winter semester, compulsory-optional
- Programme DKC-S Doctoral 2 year of study, winter semester, compulsory-optional
- Programme DKA-E Doctoral 2 year of study, winter semester, compulsory-optional
- Programme DKC-E Doctoral 2 year of study, winter semester, compulsory-optional
- Programme DKA-GK Doctoral 2 year of study, winter semester, compulsory-optional
- Programme DKC-GK Doctoral 2 year of study, winter semester, compulsory-optional
Type of course unit
Lecture
39 hod., optionally
Teacher / Lecturer
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.