A modified generic second order algorithm with fixed-time stability. (March 2021) - Tran, Xuan-Toa; Oh, Hyondong
Abstract: This paper introduces a modified second order sliding mode algorithm with fixed-time stability analysis based on the Lyapunov function approach. An existing second order sliding mode algorithm is generalized, which provides superior features on convergence rate, accuracy, and robustness against a class of perturbations. The performance of the proposed algorithm is compared with existing algorithms through designing observers first. Then, the proposed algorithm-based controller which displays the fixed-time convergence property is designed to validate its effectiveness and to confirm the theoretical analysis. Highlights: A new second order sliding mode algorithm is developed based on the Lyapunov approach. The algorithm could be applied for designing a controller, observer, or differentiator. The theoretical analysis shows fixed-time stability of the dynamic system. A simple step to estimate the upper bound of the convergence time is introduced.