Stability and Eigenvalues: What does it mean to be a "stable" eigenvalue?
ฝัง
- เผยแพร่เมื่อ 23 ต.ค. 2022
- This video clarifies what it means for a system of linear differential equations to be stable in terms of its eigenvalues. Specifically, we show that if all (potentially complex) eigenvalues have negative real part, then the system is stable. If even a single eigenvalue has positive real part, then the system is unstable.
Playlist: • Engineering Math: Diff...
Course Website: faculty.washington.edu/sbrunto...
@eigensteve on Twitter
eigensteve.com
databookuw.com
This video was produced at the University of Washington
%%% CHAPTERS %%% - วิทยาศาสตร์และเทคโนโลยี
I think it would be good to discuss the different kinds of stability, such as Lyapunov stable, asymptotically stable, exponentially stability or BIBO stable.
agreed
it's a huuge topic for control systems and kinda good for going even deeper on the subject
I also would really like to see a vid about the Lyapunov stability. Currently a topic in my vibrations class
You and Brian gave me the motivation to study the control system. Thanks, both of you.
I watched all the videos so far! That was great and easily understandable! But I really appreciate it if you explain the concept of manifolds and their application in dynamical system solutions analysis!
Finally you are the real only one who explained the eigen values in clear terms. Thank you
Maybe also worth mentioning that a "stable" matrix, so all its eigenvalues have a negative real part, is also called a Hurwitz matrix. (The discrete time equivalent to this is a Schur matrix, whose eigenvalues lie inside the unit circle of the complex plane).
This is the best video I have ever seen about this subject. Thank you so much!!
Thank you so much, Steve
Hi Steve, can you play a bit with repeated eigenvalues?
This is the last video I saw, so I don't know if in the next classes you will give such an example.
Great video...really need to appreciate the efforts you are putting in💫
Great lecture sir. Please work on some LCS lecture series also
Nevermind, I have just seen there is a video about it in the next lectures.
Thank you, Dr. Brunton.
Thank you professor...this is awesome...can you explain on how to draw Lypunov exponent with different equations using MATLAB?
I have a feeling these lectures would be helpful to understand renormalization group flow in my physics work
I've been enjoying the series... and I feel the need to ask:
How are you behind the board and writing so effectively right-to-left on your side of the board?
I have been thinking about a number of film and After Effects techniques flip video footage, however in all of those that I can think of you would still have to be writing backwards. I actually think this is filmed as simply as it appears, a large sheet of plexiglass or simply glass,, a blackout curtain, and primarily lighting from the sides. The text is in the periphery of the light cone or good diffusion scrims are being used to make the light less harsh (which we can isn't entirely enough to compensate for the strong side lighting behind the plexiglass as there are strong shadows around your nose, your philtrum, and sides of your mouth while your right and left side are pretty evenly well lit, only "valleys" symmetric to both sides end up strongly shadowed). The lighting is "highlighting" the text as it's making the text appear to fluoresce slightly with the light passing through the marker ink contrasted against the black background.
There is a glass pane in front of the camera, lit from the front (camera) side to illuminate the letters. He writes on it normally, facing the camera. The video is flipped left-to-right in post.
@@JaySmith91 Yes okay got it. I was thinking of the flip as a physical rotation which would place him between the camera and the panel. But in just a mirror flip in silico no such rotation need be contributed. Thank you. The rest with the lighting being primarily behind the panel is accurate though yeah?
Thank you Professor!
Just for completeness: not all square matrices are diagnosable, and there is repeated eigenvalues case. Maybe it was worth to add a linear algebra primer as a side note to the lectures.
You will discuss Ljapunov second method in this lectures? Nothing on repeated eigenvalues?
great teacher
Thank you very much!
What if A is dependent on time A(t)? Can I still analyze the system stability at various instants of time by analysis of the constant A(t=tfixed)? And would this stability information indicate a tendency to diverge at the time tfixed?
This issue of the unstability is the main reason why I don't deeply believe in the concept of modes and eigenvalues as a religion.
David Ruelle, in the 70's, had already seen that the concept of many many modes should be replaced by a few strange attractors.
In physics, the evanescent waves exist ( lambda negatif), but nobody has never seen a wave increasing with the distance.
Certainly, the concept of mode/eigenvalue should be replaced by the one of strange attractor.
But nobody has never succeeded to do this.
The theory of chaos has never given the slightest little engineering tool for prediction...
Interesting...
very good
Very nice
Please explain about Lyapunov equation or test
Why at 4:01 you wrote down x(0)? Where does It come from?
yup! nice! so governed by (exp)... good luck with it! giddy up pony!
Why should Polish people sit only on the left side of an airplane? Because right-half-plane poles cause instability.
Flight dynamics and control system engineer from india
So what ?
At 9:17 I hear about oscilation at frquency 'b' can someone explain what it means with a real life application example ?