Coefficient-Based Classes of Algebraic Conditions to Construct Positive Real Rational Functions

This brief deals with introducing some simple algebraic conditions ensuring the positive realness of a biproper rational function. By meeting these conditions, which specify inequality-based criteria on the coefficients of the polynomials in the numerator and denominator of a biproper function, some classes of interval positive real rational functions can be constructed. A sample application of the obtained results in feedback passivation of non-passive systems is discussed.