Data-Driven Certified Mode Detection for Switched Discrete-Time Takagi–Sugeno Systems with Adaptive Observation Window

This paper addresses active-mode detection for switched discrete-time Takagi–Sugeno systems from noisy input–output data under candidate-dependent input correction and uncertainty in data-driven observability subspaces. A lifted input–output formulation is developed in which each candidate mode is associated with a mode-dependent forced-response correction and a nominal observability subspace identified offline from representative data. Based on this construction, a practical residual criterion is introduced together with an ideal residual criterion defined by the exact residual projector. An online verifiable sufficient condition is then derived to guarantee consistency between the practical and ideal residual orderings, yielding a conservative but theorem-consistent certification mechanism. To quantify the effect of measurement uncertainty, a component-wise noise-to-signal ratio (NSR) analysis is established, leading to explicit conservative NSR bounds when signal-floor conditions are available offline. These results motivate an adaptive observation-window strategy driven by an explicit online NSR estimate. In addition, an uncertainty-corrected discernibility index based on principal angles between estimated observability subspaces is introduced to assess offline mode separability. Simulations on a switched T–S benchmark show high practical detection accuracy, sound but conservative certification, informative NSR bounds, and stable adaptive-window regulation, including under reviewer-motivated switching stress tests and baseline comparison experiments.