Eigenvalue-based algorithms for testing positive realness of SISO systems

A computational test for scalar positive real and strictly positive real functions is proposed in this paper. The input for this algorithm is state space representation, not necessarily minimal. It is derived for the discrete time problem, based on numerical stable eigenvalue computations. The test can be used in the continuous counterpart, which is in fact an improvement of an algorithm posed by Bai and Freund. Differences between the discrete and continuous time problems are also pointed out.