Third-Cycle Courses

Faculty of Engineering | Lund University

Details for the Course Syllabus for Course FRT002F valid from Autumn 2019

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  • English
  • If sufficient demand
  • to learn fundamental theory for linear time-varying dynamical systems with several inputs and several outputs.
  • Transition matrices. Controllability and observability. Realization theory. Stability theory. Operator theory. Multivariable input-output descriptions.
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

Judgement and Approach
  • For a passing grade the doctoral student must
Types of Instruction
  • Lectures
  • Exercises
Examination Formats
  • Written exam
  • Written assignments
  • Failed, pass
Admission Requirements
Assumed Prior Knowledge
Selection Criteria
  • Rugh, Wilson J.: Linear System Theory. Prentice Hall, 1996. ISBN 0134412052.
Further Information
  • Replaces FRT001F.
Course code
  • FRT002F
Administrative Information
  •  -10-27
  • it-tjo

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