Linear dynamical systems

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.

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Content

• Introduction. State equations. Linearization. Transition matrix.
• Time invariant and periodic systems. Discrete time state equations.
• Stability. Lyapunov criteria.
• Controllability and observability. Canonical state space models.
• Realizability and minimal realizations.
• Linear state feedback.

Method of evaluation
Pass/Fail grade. To get a Pass grade, the student must submit attempts to all assignments, and must also pass the final take-home exam. The final exam will be handed out on the last day of class, and the written answers will be due two weeks from then.

Course web-site

Format of course meetings
Flipped classroom.

Prerequisites
Matrix analysis, Basic ideas in Communication, Controls or Signal Processing.

Balazs Kulcsar Telephone: 031-772 1785 Email: kulcsar@chalmers.se Torsten Wik Telephone: 031-772 514685 Email: tw@chalmers.se

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.

Balazs Kulcsar Telephone: 031-772 1785 Email: kulcsar@chalmers.se Torsten Wik Telephone: 031-772 514685 Email: tw@chalmers.se