Routh Hurwitz Theorem
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, Routh Hurwitz theorem gives a test to determine whether a given polynomial is Hurwitz-stable. It was proved in 1895 and named after Edward John Routh and Adolf Hurwitz. Let f(z) be a polynomial (with complex coefficients) of degree n with no roots on the imaginary line (i.e. the line Z=ic where i is the imaginary unit and c is a real number). Let us define P0(y) (a polynomial of degree n) and P1(y) (a nonzero polynomial of degree strictly less than n)…mehr

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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, Routh Hurwitz theorem gives a test to determine whether a given polynomial is Hurwitz-stable. It was proved in 1895 and named after Edward John Routh and Adolf Hurwitz. Let f(z) be a polynomial (with complex coefficients) of degree n with no roots on the imaginary line (i.e. the line Z=ic where i is the imaginary unit and c is a real number). Let us define P0(y) (a polynomial of degree n) and P1(y) (a nonzero polynomial of degree strictly less than n) by f(iy) = P0(y) + iP1(y), respectively the real and imaginary parts of f on the imaginary line. We can easily determine a stability criterion using this theorem as it is trivial that f(z) is Hurwitz-stable iff p q = n. We thus obtain conditions on the coefficients of f(z) by imposing w(+ ) = n and w( ) = 0.