Separation principle for Caputo–Hadamard fractional‐order fuzzy systems

Abstract In this study, we propose a separation principle for Caputo–Hadamard fractional‐order fuzzy systems. Practical Mittag‐Leffler stability is introduced as a key stability concept, incorporating fractional‐order derivatives and fuzzy logic controllers. By constructing appropriate Lyapunov functions and employing linear matrix inequalities (LMIs), we derive conditions ensuring the stability of the closed‐loop system. Furthermore, an observer‐based control approach is developed to handle system uncertainties and measurement noise. This work broadens the scope to encompass practical stability criteria and generalizes the system framework to the Caputo–Hadamard fractional‐order system case. Numerical examples validate the theoretical results, illustrating the effectiveness of the proposed methods. These theoretical results may provide valuable insights and potential applications in real‐world engineering and industrial contexts.