Recurrent Sliding Mode-Based State Observer Design for a Subset of Nonlinear Systems

This paper introduces a novel Sliding Mode-Based Observer tailored for a specific subset of nonlinear systems of order <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\boldsymbol n$</tex> featuring Lipschitz nonlinearities. The study establishes stability conditions that ensure convergence of the estimation error (s) in finite time until order <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\boldsymbol n$</tex>, thus, providing an accurate state (s) estimation without the necessity for disturbance matching conditions. Furthermore, the study presents an extension of the scope of application of the proposed method to tackle a unique scenario characterized by a time-varying and non-invertible function of the output dynamics of the system model. The effectiveness of the proposed observer is showcased through simulation examples.