A class of predefined-time controllers for uncertain second-order systems

Abstract This paper proposes a novel formulation for robust predefined-time stabilisation of a class of second-order systems with matched perturbations. The presented approach allows designing a family of controllers that enforce a predefined-time sliding motion, even in the presence of unknown but bounded perturbations, such that, during the sliding motion, the state slides to the origin in predefined-time. Consequently, the origin of the closed-loop system is globally predefined-time stable. The analysis and design of the proposed controllers rely on the Lyapunov framework and a novel class of nonlinear functions, providing stability and robustness conditions for the closed-loop system. Finally, numerical simulations are conducted to highlight the reliability of the proposed scheme.

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