Om kursen
About the course
Aims
Linear systems theory is one of the fundaments upon which many methods for control systems analysis and design are based. This course aims at consolidating knowledge about linear, time-invariant systems to multivariable time-varying systems (LTV). One of the course objectives is to provide a solid theoretical basis for linear, finite-dimensional systems, necessary to follow much of the scientific literature in connected fields.
Content
Introduction. State equations. Linearization. Transition matrix.
Time variant and periodic systems. Discrete time state equations.
Stability. Lyapunov criteria.
Controllability and observability. Canonical state space models.
Realizability and minimal realizations. Input output models.
Linear state feedback.
Method of evaluation
Pass/Fail grade. To get a Pass grade, the student must submit attempts to all assignments and exercises, must also pass the final take-home exam, and actively participate in lectures. The final exams will be handed out on the last day of class and the submissions are due two days later.
Format of course meetings
Blended learning techniques: flipped classrooms, quizzes, discussion panels, weekly meetings, weekly exercises, hand in assignments.
Prerequisites
Matrix analysis, basics in communication, systems and control background, basics in signal processing.
More information
The course is offered every other year (even-numbered calendar year). Canvas is used as online learning platform. For more information contact
Balazs Kulcsar telephone: 031-772 1785 email: kulcsar@chalmers.se or Torsten Wik telephone: 031-772 514685 email: tw@chalmers.se
Literature
Core texts
W. J. Rugh, Linear system theory, second edition, John Wiley, 1996.
R. W. Brockett, Finite dimensional linear systems, John Wiley, 1970.
J. M. Maciejowski, Multivariable feedback design, Addison-Wesley, 1989
Ancilliary texts
V. I. Arnold, Ordinary differential equations, MIT press/ Springer Verlag, 1973/1991.
J. W. Polderman and J. C. Willems, Introduction to mathematical systems theory, Springer Verlag, 1998.
J. C. Doyle, B. A. Francis, and A. R. Tannenbaum, Feedback control theory, McMillan, 1992.
T. Kailath, Linear systems, Prentice hall, 1980.
Lecturer
Balazs Kulcsar Telephone: 031-772 1785 Email: kulcsar@chalmers.se Torsten Wik Telephone: 031-772 514685 Email: tw@chalmers.se
