Linear Systems
Linjära system

FRT002F, 9 credits

Valid from: Autumn 2019
Decided by: it-tjo
Date of establishment: 2016-10-27

General Information

Division: Automatic Control
Course type: Third-cycle course
Teaching language: English

Aim

to learn fundamental theory for linear time-varying dynamical systems with several inputs and several outputs.

Goals

Knowledge and Understanding

For a passing grade the doctoral student must

• understand how linear timevarying systems can be represented in different ways and how the relationships between the representations look like
• understand how controllability and observability can be analyzed with several different methods
• understand how realizations can be performed starting from transfer functions or Markov parameters
• be able to define and analyze various stability notions for linear timevarying systems
• be able to interpret least-squares problems in terms of linear operators and adjoint operators

Competences and Skills

For a passing grade the doctoral student must

• be able to linearize a timevarying system along a trajectory
• be able to determine Kalman's decomposition and a minimal realization of a system
• be able to verify exponential stability of a linear time-varying system using a Lyapunov function
• be able to determine the poles and zeros, including multiplicities, of a multivariable system

Course Contents

Transition matrices. Controllability and observability. Realization theory. Stability theory. Operator theory. Multivariable input-output descriptions.

Course Literature

Rugh, Wilson J.: Linear System Theory. Prentice Hall, 1996. ISBN 0134412052.

Instruction Details

Types of instruction: Lectures, exercises

Examination Details

Examination formats: Written exam, written assignments
Grading scale: Failed, pass
Examiner:

Admission Details

Further Information

Replaces FRT001F.

Course Occasion Information

Contact and Other Information

Course coordinators: