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300s School/ME 2016 - Nonlinear Dynamical Systems 1/2024-10-28 Stability.md
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@ -13,3 +13,5 @@ For autonomous systems. Basically, adhere to a path for distrubances.
$x^*$ is a phase path or equilibrium point whose stability is in question. $x^*$ is a phase path or equilibrium point whose stability is in question.
This is a solution of $\dot x = X$ This is a solution of $\dot x = X$
### 'Half-path' or 'Half-orbit' or 'Semi-orbit' ### 'Half-path' or 'Half-orbit' or 'Semi-orbit'
1. Start on $a^*$ and travel on half-path $\mathcal{H}^*$
2. $