september 18


  • What operators can appear as state transition (fundamental) ones, \(\Phi(t)\)?
  • For LTVs, any operator \(\Phi\) with \(\det(\Phi)>0\) can be a fundamental solution; for LTIs the situation is far more complicated (say, the diagonal matrix with \(-1, -2\) on the diagonal cannot be a fundamental solution.

  • Dual evolution.

Stability of linear systems

Lyapunov stability, asymptotic stability, global asymptotic stability – definitions.

Global asymptotic stability for LTI.

Hurwitz operators. Multiple eigenvalues and Jordan normal forms.

Lyapunov’s direct method

2 Responses to september 18

  1. Anonymous September 24, 2014 at 10:14 pm #

    Is it possible to post some examples for each topic. The examples from the lecture note is not enough at all.

    • yuliy September 24, 2014 at 11:52 pm #

      I will update this as time permits. If anyone volunteers (for some bonus points) to typeset their notes in LaTeX, this would help.

Leave a Reply