Input Output Stability Analysis of Delayed Descriptor Systems According to Free Weighting Matrices

This study’s main goal is to examine the stability of descriptor systems with time-varying delays. One approached this investigation utilizing an input–output methodology centered around a three-term approximation model. Within this context, a novel delay-dependent condition was developed, integrating the concept of "free-weighting matrices". It’s worth noting that while incorporating weighting matrices could be similar to introduce flexibility into the condition, the obtained results reveal that this is not always the case. In fact, the inclusion of weighting matrices can sometimes introduce additional complexity rather than granting more freedom to the system. As a result, the paper will present two distinct developed conditions: where the first is incorporating weighting matrices, while the second is not. Both of these established conditions are formulated as linear matrix inequalities, which are applied to facilitate analysis and computation. In the concluding sections of this paper, we will provide numerical examples to illustrate the practicality, effectiveness, and validity of both of these developed conditions, offering insights into their real-world applicability. © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2025.