\(\def\Real{\mathbb{R}}\def\Comp{\mathbb{C}}\def\Rat{\mathbb{Q}}
\def\Field{\mathbb{F}}
\def\Fun{\mathbf{Fun}}
\def\e{\mathbf{e}}
\def\f{\mathbf{f}}\)
Remarks
- What operators can appear as state transition (fundamental) ones, \(\Phi(t)\)?
- Dual evolution.
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.
Stability of linear systems
Examples.
Lyapunov stability, asymptotic stability, global asymptotic stability – definitions.
Global asymptotic stability for LTI.
Hurwitz operators. Multiple eigenvalues and Jordan normal forms.
Is it possible to post some examples for each topic. The examples from the lecture note is not enough at all.
I will update this as time permits. If anyone volunteers (for some bonus points) to typeset their notes in LaTeX, this would help.