\(\def\Real{\mathbb{R}}\def\Comp{\mathbb{C}}\def\Rat{\mathbb{Q}}
\def\Field{\mathbb{F}}
\def\Fun{\mathbf{Fun}}
\def\e{\mathbf{e}}
\def\f{\mathbf{f}}\)
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.
2 Responses to september 18