abstract
- This paper presents a novel exponent structure for an arbitrary-order homogeneous differentiator designed to balance noise attenuation and derivative estimation accuracy in the presence of noisy measurable signals. By tuning the homogeneity degree d, the proposed differentiator can operate over a range that covers both high-gain and Levant¿s differentiators, leveraging an almost linear exponent behavior to achieve superior trade-offs between state estimation accuracy and noise resilience. In contrast to existing approaches, where the exponent variation grows exponentially with the differentiator order degrading derivative estimation generating oscillations in presence of noise, the proposed structure can effectively balance the estimation accuracy and smoothness. The method is validated via Lyapunov-based stability analysis and comprehensive simulations/experiments, demonstrating enhanced performance over existing homogeneous differentiators in noisy scenarios.