Step-by-step implicit discrete super-twisting differentiator for input-output linearizable nonlinear systems

The aim of this study was to design a step-by-step numerical differentiator for a class of discretized version of a n-th chain-of-integrator system based on the application of the implicit discretization of the super-twisting algorithm (STA). The high-order differentiator reconstructed the non-measurable states of an input-output linearizable systems. The gains of the observer were calculated based on the application of a class of generalized functions. The convergence analysis showed that all the states in the linearized system achieved an invariant set with a predefined size. The existence of this invariant set depends on the uniqueness of the solution for the generalized function. A simple interpretation of a possible exact reconstruction of the non-measurable states of the implicit discretized form. The application of the implicit discretized STA served to design a class of observer for the microalgae culture system.