Characterizations and stable tests for the Routh–Hurwitz conditions and for total positivity Original Research Article

Given a polynomial of degree n, a test of image elementary operations and growth factor 1 is presented in order to check the Routh–Hurwitz conditions. This optimal growth factor guarantees that the test presents better stability properties than other known tests. We also present a test of image elementary operations and growth factor 1 in order to check if a matrix is strictly totally positive. Finally, totally positive matrices are characterized by their symmetric-triangular decompositions.