# september 18

$$\def\Real{\mathbb{R}}\def\Comp{\mathbb{C}}\def\Rat{\mathbb{Q}} \def\Field{\mathbb{F}} \def\Fun{\mathbf{Fun}} \def\e{\mathbf{e}} \def\f{\mathbf{f}}$$

##### Remarks
• What operators can appear as state transition (fundamental) ones, $$\Phi(t)$$?
• 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

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

#### Global asymptotic stability for LTI.

Hurwitz operators. Multiple eigenvalues and Jordan normal forms.

### 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.