4 ms·
Widely known in the controls engineering world for the last hundred years as 'anything is linear if you zoom in far enough'
by idiotsecant 3y ago
Widely known in the controls engineering world for the last hundred years as 'anything is linear if you zoom in far enough'
- vitus 3y agoWell, subject to certain constraints. You aren't guaranteed that your equilibria behave the same in the linearization of a nonlinear system if your Jacobian has any eigenvalues with real part of 0. https://en.wikipedia.org/wiki/Hartman%E2%80%93Grobman_theorem https://en.wikipedia.org/wiki/Hartman%E2%80%93Grobman_theore...
- new_username01 3y agoIt's amazing how many ideas I've seen being "rediscovered" these days from control theory.
- kqr 3y agoWait isn't that just an application of Taylor expansion which analysis has known about for several hundreds of years?
- f1shy 3y agoTaylor is only for some functions, must be continuos and differentiable to n grades. In control theory you break the functions, so discontinuities can also be considered.
- rcfox 3y agoAlternatively, anything is linear if you add enough dimensions.