Adaptive finite time high‐order sliding mode observer for non‐linear fractional order systems with unknown input

Abstract In the present study, the concept of homogeneity is extended for fractional‐order systems by applying Caputo's derivative definition. Then, a fractional‐order high‐order sliding mode observer is proposed for a class of nonlinear fractional‐order single input–output systems. The asymptotic stability of the observer is analyzed and its finite‐time stability is derived through homogeneity property followed by obtaining a bound for its convergence time. To improve performance and reduce the chattering phenomenon, a tuning rule is presented through Lyapunov stability criterion using finite dimensional approximation of diffusive representation of the system. Finally the efficiency of the proposed method is investigated through two simulation examples.