Stability Analysis of Incommensurate Fractional-Order Systems with Multiple Time Delays

This paper explores the stability of incommensurate fractional-order models. Building on previous work that introduced a method for assessing stability and calculating delay margins for single delay models, this study extends the analysis to models with multiple delay parameters. The proposed method assumes all delayed signals within the model act as disturbances. By employing the generalized smallgain theorem, stability conditions are established. These conditions rely on the H∞ norm and frequency analysis, resulting in final outcomes that depend on the fractional orders of the model. Importantly, the derived stability condition is independent of the delay parameter values.