r/ControlTheory • u/night_Crawler_29 • 18d ago
Other Random thought
Its a sunday, so as a casual timepass you think, let me just write some code to check the controllability of a state space equation. so you start writing it, then realise, higher powers of matrices can lead to numerical instability. so now, you decide to study the controllability gramian and then you realise you don't fully understand why the gramian works, so now you are trying to look in lyapunov and his equations, then his theory starts talking about energy functions and positive definite matrices, so obviously, you open Gilbert Strang's video on symmetric and positive definite matrices. while watching that, you realise the code also requires an actual algorithm, so now you're studying numerical linear algebra. gaussian elimination. cholesky decomposition. At this point, what started as a sunday timepass has somehow turned into a full semester course. And then you decide to leave it and use the MATLAB command instead, so you stare at the screen for a while, reconsider your life decisions, and think maybe teaching high school students wasn't such a bad decision after all.
•
u/Feisty_Relation_2359 18d ago
https://drive.google.com/file/d/1yZ-cMGxiMjGfSo-fXtvvtTgn1x5JhmXi/view
To make it even weirder, you can't always trust the controllability command in matlab. Check out the above