Fault diagnosis and tolerant strategy for MIMO system based on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si8.svg" display="inline" id="d1e1128"><mml:mi>ν</mml:mi></mml:math>-gap metric

The coupled relationship between inputs and outputs in multiple-input multiple-output (MIMO) systems, as well as the multiplicative uncertainties caused by multiplicative faults, increases the complexity of fault diagnosis (FD) and fault-tolerant control (FTC). Research has indicated that coprime factor uncertainties are suitable for modeling multiplicative uncertainties. This paper presents an FD and FTC strategy for MIMO systems based on the ν-gap metric technique within the coprime factorization framework. In the offline phase, the ν-gap metric-based hierarchical clustering method is designed to classify fault samples. Next, core systems and boundary systems are calculated for each fault category, and corresponding residual compensation controllers are designed. In the online phase, by computing the relevant ν-gap metric values, the fault severity of the real-time system is determined, and the core system with similar dynamic behaviors is identified. This FD result drives the switching of residual compensation controller, achieving FTC and ensuring system stability and robustness. This strategy eliminates the need for online solving of fault-tolerant controller, saving computational resources. Finally, the ν-gap metric-based FD and FTC strategy is validated with simulations on a three-phase voltage source inverter system.