Some conditions for almost strict positive realness

The requirement for an `almost strictly positive real´ (ASPR) system as a part of the stability analysis of the `simplified adaptive controller´ is considered. This property is examined for minimum-phase system and is related to output stabilizability and to the steady-state Riccati equation. A numerical procedure is developed to determine whether a given system is ASPR, and its application is illustrated with an example. The algorithm exhibits excellent convergence for all minimum-phase cases with collocated sensors/actuators, but does not perform as well in the presence of small perturbations in the collocated output matrix C. However, as is common in numerical procedures of this sort, failure of the algorithm does not prove that a given system is not ASPR