A Novel Stability Approach for Time Delayed Descriptor Systems: Ssg Technique and Three-Term Input-Output Approximation

The main objective of this study is to investigate the stability of descriptor systems with time-varying delays. The analysis is performed using an input-output approach based on a three-term approximation model. This paper presents a new condition formulated as a linear matrix inequality (LMI), which is validated through a numerical example provided towards the end. This example illustrate the effectiveness and validity of the proposed theorem, offering comparisons with existing results from the literature. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2026.