Stability of linearisations using Lyapunov functions

We sketch out the method for proving local asymptotic stability based on eigenvalues of linearisations using Lyapunov theory

[@ibrahimalotaibi2399]

Dr. Richard, Thank you for sharing and simplifying such complex foundations in nonlinear control theories. Without these illustrations provided by Dr.Richard, you can not even imagine the level of complexity in the references to furnish and deliver such fundamentals. I recall during my Ph.D., I spent weeks and weeks trying to understand the contents delivered by Dr. Richard in less than 20 Minutes.

[@richard_pates]

You're very welcome. Thank you so much for your kind words, I really appreciate it!

[@mberoakoko24]

@@richard_pates I cannot access your lecture notes sir... I apparently need a login.

[@joelsanchez7963]

Hi Richard, I am Joel from Argentina and I am currently studying A&C in Germany.. Your videos are really useful, I really appreciate your dedication and effort to help students ! I will recommend your KZbin channel with my classmates, wish you a incredible and successful future

[@richard_pates]

Thank you Joel! Your kind words mean a lot. I wish you the same!

[@peter_b.1337]

Thank you for this lecture! There are something which is unclear for me. 1. while we calculating V_dot we see that gradient of V is P*x. Then is there a mistake in the second term where nabla V is expressed as A*x? 2. How we can manipulate epsilon? Isn't it depends on dynamics only?

[@gw1284]

Prof, are your lecture notes posted online?like to study it besides watching your lecture video, Thanks

[@janlucaloettgen8073]

Thanks for this series, its fantastic, and helping me learn control topics not taught at my University. The lecture notes you refer to, are they publicly available? If not could you recommend a text book that this course is based on?

[@richard_pates]

Everything should be publicly available. Sometimes there are problems with old links breaking (this is a real problem with the platform we use to structure our courses). However if you check the about section on my channel, or my webpage (richardpates.com) I'll try to keep the correct links there. As for text books, Khalil's 'Nonlinear systems' is a really good resource - I would recommend that

[@eBrunoro]

I understand that x is a vector. So, what does "x → 0" mean? If it is a limit, by which path does the vector x tend to zero? Does it matter?

[@richard_pates]

good question - I was being rather sloppy. We should really write something like lim_{r->0} sup_{x:||x||

[@YorickVandePaar]

Shoutout to all my dreamers