LMI-Driven Reachability Analysis for Fuzzy Model-Based Nonlinear Systems Subject to Norm-Bounded Input Perturbations

In this paper, we study the reachability analysis of fuzzy model-based nonlinear systems subject to norm-bounded input perturbations. While reachability analysis has been extensively studied in safety-critical control and verification, computing reachable sets for nonlinear systems remains challenging due to inherent computational and analytical complexities. To address this issue, we propose a Lyapunov-based reachability framework formulated via linear matrix inequalities (LMIs) within fuzzy modeling techniques. This framework represents a nonlinear system as a weighted summation of linear subsystems, while explicitly accounting for norm-bounded model approximation errors, enabling the effective application of linear control techniques. The proposed LMI-driven framework yields a Lyapunov function whose level sets provide an ellipsoidal over-approximated reachable set under both model approximation errors and norm-bounded perturbations. The effectiveness of the proposed framework is demonstrated using the attitude dynamics of a quadrotor unmanned aerial vehicle (UAV).