LMIs in Control/Click here to continue/Applications of Non-Linear Systems/Chebyshev Polynomials

Chebyshev Polynomials

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Required data

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A univariate Polynomial whose SOSINEQ range specification is desired

The Problem

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Let   be a univariate polynomial of degree   being the coefficient of  .

 , subject to:
 .

Formulation

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The absolute value constraint can be easily rewritten using two inequalities, namely:

 .

Solution

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The optimal solution is  , with   being the n-th Chebyshev polynomial of the first kind.


Example

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Code example in SOStools probably worthwhile!

Reference

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SOS tools manual: https://sums-of-squares.github.io/sos/

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SOS Basics

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