Eigenvalue-based characterization and test for positive realness of scalar transfer functions

An eigenvalue-based characterization of positive realness of transfer functions of a single-input single output time-invariant linear system is derived. Based on this characterization, we propose an efficient computational procedure to determine if a given transfer function is positive real. The input for this eigenvalue-based test is any given, not necessarily minimal, state-space representation of the linear system. The test only involves standard matrix computations, such as computing eigenvalues of a matrix or a matrix pencil. Results of numerical experiments are reported.