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.