Index of Performance as a Degree of Controllability for Vibrating String With an Internal Point Control

Abstract

Controllability properties for distributed parameter systems are often nonrobust in the sense that they can change for arbitrarily small variations of parameters, which often leads to unpractical results. In the case of a vibrating string with an internal point control, we define and study a continuous function of a structural parameter that may be interpreted like an index of performance. From its regularity properties, this function exhibits connections with the concept of controllability. This analysis does not pretend to be exhaustive but may be considered as a tentative, to be extended to more general situations, in the aim to reduce the gap between certain theoretical properties of vibrating distributed parameters systems and their corresponding practical counterparts.