Logo ČVUT
Loading...
CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2011/2012

Theory of Dynamical Systems

Login to KOS for course enrollment Display time-table
Code Completion Credits Range Language
A3M35TDS Z,ZK 8 4+2c Czech
Lecturer:
Vladimír Kučera (gar.)
Tutor:
Jiří Cigler, Petr Hušek, Samuel Prívara, Ondřej Šantin, Zdeněk Váňa
Supervisor:
Department of Control Engineering
Synopsis:

The purpose of this course is to introduce mathematical tools for the description, analysis, and partly also synthesis, of dynamical systems. The focus will be on linear time-invariant multi-input multi-output systems and their properties such as stability, controllability, observability and state realization. State feedback, state estimation, and the design of stabilizing controllers will be explained in detail. Partially covered will be also time-varying and nonlinear systems.

Some of the tools introduced in this course are readily applicable to engineering problems such as the analysis of controllability and observability in the design of flexible space structures, the design of state feedback in aircraft control, and the estimation of state variables. The main motivation, however, is to pave the way for the advanced courses of the study program.

The prerequsites for this course include undergraduate level linear algebra, differential equations, and Laplace and z transforms.

Requirements:
Syllabus of lectures:

1.Systems and signals. Linear and time-invariant systems. Differential and difference systems.

2.The concept of state, state equations.

3.Solving the state equations, modes of the system. Equivalence of systems. Continuous-time, discrete-time, and sampled-data systems.

4.Lyapunov stability, internal and external stability properties of linear systems.

5.Reachability and controllability of systems.

6.Observability and constructibility of systems. Dual systems.

7.Standard forms for systems, Kalman's decomposition.

8.Internal and external descriptions of systems, impulse response and transfer function. Poles and zeros of systems.

9.State realizations of external descriptions. Minimal realizations, balanced realizations.

10.State feedback, state regulation, pole assignment.

11.Output injection, state estimation.

12.Interconnection of systems, feedback controllers, stabilizing controllers.

13.State representation of stabilizing controllers

14.Separation property of state regulation and estimation.

Syllabus of tutorials:

For each exercise session, a list of exercises from the previous lecture is made available that the student is requested to solve and deliver the solutions prior to the session. Each session begins by a short test, then the exercise solutions will be checked and discussed, and difficult points will be explained.

Study Objective:
Study materials:

P.J. Antsaklis, A.N. Michel: A Linear Systems Primer. Birkhäuser, Boston 2007. ISBN-3: 978-0-8176-4460-4

Note:
Time-table for winter semester 2011/2012:
06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00
Mon
roomKN:E-2

07:30–09:00
(lecture parallel1
parallel nr.101)

Karlovo nám.
Laboratoř PC
roomKN:E-2
Prívara S.
09:15–10:45
(lecture parallel1
parallel nr.102)

Karlovo nám.
Laboratoř PC
roomKN:E-2
Šantin O.
11:00–12:30
(lecture parallel1
parallel nr.103)

Karlovo nám.
Laboratoř PC
roomKN:E-2
Cigler J.
12:45–14:15
(lecture parallel1
parallel nr.104)

Karlovo nám.
Laboratoř PC
roomKN:E-2
Váňa Z.
14:30–16:00
(lecture parallel1
parallel nr.105)

Karlovo nám.
Laboratoř PC
roomKN:E-2
Hušek P.
16:15–17:45
(lecture parallel1
parallel nr.106)

Karlovo nám.
Laboratoř PC
roomKN:E-2

18:00–19:30
(lecture parallel1
parallel nr.107)

Karlovo nám.
Laboratoř PC
Tue
roomT2:C3-135
Kučera V.
11:00–12:30
(lecture parallel1)
Dejvice
Posluchárna
Fri
Thu
roomT2:C3-340
Kučera V.
11:00–12:30
(lecture parallel1)
Dejvice
Posluchárna
Fri
Time-table for summer semester 2011/2012:
Time-table is not available yet
The course is a part of the following study plans:
Generated on 2012-7-9
For updated information see http://bilakniha.cvut.cz/en/predmet12539304.html