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Generate the Hurwitz matrix of a univariate polynomial
ResourceFunction["HurwitzMatrix"][poly,x] gives the Hurwitz matrix of poly, treated as a polynomial in x. |
Generate the Hurwitz matrix of a polynomial:
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Generate the Hurwitz matrix from a polynomial with numeric coefficients:
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Generate the Hurwitz matrix from a polynomial with symbolic coefficients:
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Use HurwitzMatrix to check the stability of a polynomial:
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Verify stability by computing the roots of the polynomial:
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A polynomial whose roots all have negative real parts:
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The corresponding Hurwitz matrix has principal minors that are all positive:
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Apply a Möbius transformation to the polynomial:
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The transformed polynomial has a Schur matrix that is positive definite. That is, all of the roots of the transformed polynomial are within the unit disk:
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