CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2024/2025

# Linear Systems

Code Completion Credits Range Language
B3M35LSY1 Z,ZK 6 4P+2C Czech
Garant předmětu:
Petr Hušek
Lecturer:
Petr Hušek
Tutor:
Denis Efremov, Petr Hušek, Viktor-Adam Koropecký
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:

There are no prerequisities however basic knowledge of linear algebra is expected.

Syllabus of lectures:

Systems and signals. Linear and time-invariant systems. Differential and difference systems. The concept of state, state equations.

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

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

Reachability and controllability of systems.

Observability of systems. Dual systems.

Standard forms for systems, Hautus' tests, Kalman's decomposition.

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

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

State feedback, state regulation, pole assignment, LQ regulator.

Output injection, state estimation, LQ estimator.

Interconnection of systems, feedback controllers, stabilizing controllers.

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:

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.

Study materials:

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

Note:
Further information:
https://moodle.fel.cvut.cz/course/view.php?id=6134
Time-table for winter semester 2024/2025:
 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 roomKN:E-26Hušek P.09:15–10:45(lecture parallel1parallel nr.101)Karlovo nám.Laboratoř TŘ2roomKN:E-26Hušek P.11:00–12:30(lecture parallel1parallel nr.102)Karlovo nám.Laboratoř TŘ2roomKN:E-23Hušek P.12:45–14:15(lecture parallel1parallel nr.103)Karlovo nám.Laboratoř ABroomKN:E-26Hušek P.14:30–16:00(lecture parallel1parallel nr.104)Karlovo nám.Laboratoř TŘ2 roomT2:D3-309Hušek P.11:00–12:30(lecture parallel1)DejviceT2:D3-309 roomT2:D3-309Hušek P.11:00–12:30(lecture parallel1)DejviceT2:D3-309
Time-table for summer semester 2024/2025:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2024-05-25
Aktualizace výše uvedených informací naleznete na adrese https://bilakniha.cvut.cz/en/predmet6771806.html