Linear Dynamical Systems

Om kursen

Learning the state space and frequency response methods of analysing linear systems. Learn- ing basic ideas needed for further study of nonlinear control, adaptive control, and multivariable control design methods such as H∞ synthesis.

  • Time domain Analysis: Linear differential equations with (i) constant coefficients, (ii) time-varying especially periodically varying coefficients. Controllability, Observability, State feedback and output feedback. Realizations from weighting patterns, and minimal realizations.
  • Least squares theory: Minimization in inner product spaces, Spectral factorization.
  • Frequency response techniques: Smith-McMillan form, Multivariable poles and zeroes. Matrix fraction description and Youla Parametrization. Introduction to multivariable control synthesis.
  • Stability: Lyapunov equation, Circle criterion, Kalman-Yakubovich-Popov lemma, Multi- variable Nyquist criterion and Gershgorin bands. Stability of time-varying, and periodically varying systems.
Method of evaluation
Pass/Fail grade. To get a Pass grade, the student must submit attempts to all six 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
Lectures by the instructor.

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

Mer information

Bo Egardt
Telephone: 031-772 3711


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.


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