Probabilistic MIMO Disk Margin Assessment of an eVTOL Controller Using Subset Simulation

Electric Vertical Take-Off and Landing aircraft are key enablers for Urban Air Mobility, yet their complex flight dynamics pose significant challenges for flight control design and certification. Regulatory authorities such as EASA require that catastrophic failure conditions remain extremely improbable $\left(10^{-7}-10^{-9}\right.{}$ per flight hour), necessitating rigorous stability assessments. Traditional Single-Input Single-Output (SISO) stability margins are inadequate for Multi-Input Multi-Output (MIMO) systems, and existing robustness margin analyses often assume uncertainties that lack physical interpretability. Moreover, direct Monte Carlo simulation is computationally prohibitive for estimating such rare-event probabilities. This paper presents a probabilistic margin assessment framework for eVTOL controller during the safety-critical hover phase. The approach integrates three key components: (1) MIMO Disk Margin analysis to consider multi-channel coupling and simultaneous gain and phase variation; (2) physical parametric uncertainties injected into a high-fidelity nonlinear model; and (3) apply the Subset Simulation method to efficiently compute the probability of disk margin violations below safety thresholds. The results demonstrate that the proposed method achieves a significant speedup over Monte Carlo while capturing failure probabilities below 10^-7. The results also reveal the dominant contributors to disk margin failure.