Finite- and fixed-time differentiators utilising HOSM techniques

Finite- and fixed-settling time of real-time differentiators utilising a higher-order sliding mode (HOSM) observer based on both non-recursive and recursive algorithm formulations are studied using constant observer gains. Fixed convergence time estimation is achieved independent of initial conditions of the differentiation errors. The corresponding convergence/settling times are estimated. The HOSM differentiators are compared with the ideal differentiation formulation and MATLAB's differentiator. The analysis incorporates input noise to demonstrate via simulations the improved performance for real-time noisy input signals.