An Algorithm to Verify the Positive Realness of Transfer Function Matrices

The positive realness of transfer function matrices is an important concept in absolute stability theory and passive systems. In literature, some necessary and sufficient conditions for a positive real transfer function matrix had been obtained. However, it is not easy to verify these conditions. In this paper, we will present a direct and feasible algorithm to verify the positive realness of the transfer function matrices. The algorithm is imposed on the coefficients of the rational functions and the analysis techniques are based on real algebraic geometry and mathematics mechanization method.