The Nyquist Criterion, Stability Notions, and The Argument Principle

Описание: Stability is one of the most important concepts in control theory. We cover three notions of stability for LTI systems; BIBO stability, L2 Stability, and Exponential Stability. This involves Laplace transforms, the Pailey Wiener Theorem, the Argument Principle, Contour Mappings, and counting how many times a string wraps around the point -1.


//Additional Reading
Nyquist Stability Criterion slides by Dr. Lenari http://www.diag.uniroma1.it//~lanari/...


//Exercises




//Watch Next
The Other Pailey Wiener Space and Nyquist Sampling Theorem    • Sampling theory and why I reject a lot of ...  
The Pailey Wiener Theorem    • The Paley Wiener Theorem and the Inversion...  
The Analyticity of the Laplace transform    • Morera's Theorem in Practice - Laplace Tra...  

Undergraduate Intro to the Laplace Transform    • MAP2302 - Definition of the Laplace Transf...  

A Mature Look at the Laplace transform    • Introduction to the Laplace Transform  
Introduction to Control Theory    • Introduction to Control Theory  


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Under the Impression by Tape Machines
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//Books
Nonlinear Systems - Khalil https://amzn.to/32Zyk8E
Functions of One Complex Variable - Conway https://amzn.to/3M0snu6


Real and Complex Analysis - Rudin https://amzn.to/3riipvZ
Real Analysis - Folland https://amzn.to/3ogVuiG
Fundamentals of Differential Equations - Nagle, Saff, and Snider https://amzn.to/3qeGD9C


Advanced Mathematical Analysis - Beals https://amzn.to/3fn2jdP
From Vector Spaces to Function Spaces - Yutaka Yamamoto https://amzn.to/3sU2CVj
Feedback Control Theory - Doyle, Francis, Tannenbaum https://amzn.to/3HFvuov
Pick Interpolation and Hilbert Function Spaces - Agler and McCarthy https://amzn.to/3EOJU3K
Modern Control Systems - Dorf and Bishop https://amzn.to/331JQAm

// MATLAB Code
https://bitbucket.org/joelrosenfeld/n...


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0:00 Start
0:32 What is Stability?
1:51 Bounded Inputs
2:51 Using powerful tools for an easy proof of stability
5:41 The Argument Principle
8:05 The Nyquist Contour
9:16 Contours Prove Stability