A Trisection Algorithm for Estimating Distance Measures for Strong Observability and Strong Detectability

For reliably analyzing the properties of strong observability and strong detectability of a system, continuous distance measures can be used. When calculating these measures, it is necessary to find the global minimum of a nonconvex target function. The main contribution of this article is an optimization algorithm that guarantees to find this global minimum in a fast and efficient way by exploiting the special structure of the optimization problem. Using this optimization algorithm, the distance measures can be reliably calculated. The numerical properties and the usefulness of the algorithm in practical applications are illustrated by means of a numerical example.