Markov parameter characterization of the strict positive real problem

Suppose that a rational function is defined by a Laurent series, the coefficients of which are known. Several criteria are given in terms of these coefficients (the Markov parameters of ) to ensure that for all real . The criteria are defined by using a Cauchy index formulation of the ratio of two rational functions, and they are of three types-involving a Routh-like table with first two rows initialized using the coefficients, and Hurwitz and Bezout matrices with entries which are the coefficients themselves, or integral expressions in the coefficients. The matrix positive real property is also investigated.