Pick Interpolation in MATLAB @JoelRosenfeld

Uploaded April 2022 | Updated September 2026, 16 hours ago

Here we code up Nevanlinna Pick interpolation from H infinity control in MATLAB, from scratch. The Nevanlinna Pick Interpolation theorem is a key part of robust control theory and sensitivity minimization.

//MATLAB Code

bitbucket.org/joelrosenfeld/pick-interpolation-algorithm/src/master

//Additional Reading
Garnett's "Bounded Analytic Functions" - amzn.to/3KwjE1w
From Vector Spaces to Function Spaces - Yutaka Yamamoto amzn.to/3sU2CVj
Feedback Control Theory - Doyle, Francis, Tannenbaum amzn.to/3HFvuov

//Watch Next
Bode Plots in Neuroscience and Control Theory youtu.be/fVivGKGhbqg
The Analyticity of the Laplace transform youtu.be/FIMkbFQL6XM
Introduction to Control Theory youtu.be/0v4WFmOm764

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Nonlinear Systems - Khalil amzn.to/32Zyk8E
Functions of One Complex Variable - Conway amzn.to/3M0snu6

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

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

// MATLAB Code
bitbucket.org/joelrosenfeld/nyquist-criterion-video-figures/src/master

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0:00 Introduction
1:15 Get the data
2:54 One Point with Blaschke Factors
6:06 Iterating Transformations
9:16 Unpacking the full interpolation problem
12:26 The Proof of the Nevanlinna Pick Interpolation Theorem

Numerical Analysis - The Gradient Descent Method

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$Convolutions and Anti Derivatives of Distributions The definition of the convolution of two distributions arises from that of regular distributions and in turn, the convolution of functions. We leverage this definition to give a definition of an antiderivative of a distribution, and we determine the related Laplace transform property of both of these operations. //Additional Reading Zemanian - An Introduction to Generalized Functions and the Generalized Laplace and Legendre Transformations (JSTOR) https://www.jstor.org/stable/2027808?seq=1#metadata_info_tab_contents (SIAM) https://epubs.siam.org/doi/abs/10.1137/1010001?journalCode=siread //Exercises - Show that differentiation is a continuous operation on L. - Show that 1/n phi(t/n) e^{-st} goes to zero in L (i.e. with respect to each seminorm) as n goes to infinity for every s in C. //Watch Next The Schwartz Space (Full Lecture) https://youtu.be/StzEO8B1pFY Undergraduate Intro to the Laplace Transform https://youtu.be/mJSqt7nchRQ Introduction to Control Theory https://youtu.be/0v4WFmOm764 Fixed Point Iteration - Loki gets slapped 16 times for SCIENCE https://youtu.be/_I790SqNDjs //Music Provided by Epidemic Sound Late Nights - Daxten bam bam - Yomoti Tiny Things - Giants Nest Use this referral link to get a 30 day free trial with Epidemic Sound for your YouTube channel: https://www.epidemicsound.com/referral/644nao //Books 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 Nonlinear Systems - Khalil https://amzn.to/32Zyk8E Modern Control Systems - Dorf and Bishop https://amzn.to/331JQAm Fundamentals of Differential Equations - Nagle, Saff, and Snider https://amzn.to/3qeGD9C //Recording Equipment Canon SL3: https://amzn.to/3nZ11KU Canon T6i: https://amzn.to/3FUpkQh Rode VideoMic: https://amzn.to/3lhldGa Blue Yeti Microphone: https://amzn.to/3I1y88N Yeti Nano Microphone: https://amzn.to/3I1mriA SanDisc 256GB SD Card: https://amzn.to/3E3LOOr Neewer 5600K USB LED Lights: https://amzn.to/3xvB9cN Neewer 18 inch Ring Light: https://amzn.to/2ZvgCsc Camera Power Adapter: https://amzn.to/3D3upUu DISCLAIMER: The links above in this description may be affiliate links. If you make a purchase with the links provided I may receive a small commission, but with no additional charge to you :) Thank you for supporting my channel so that I can continue to produce mathematics content for you!$

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