A Novel Approach to Fixed-Time Stabilization for a Class of Uncertain Second-Order Nonlinear Systems

Abstract

This paper is concerned with the problem of fixed-time stabilization for a class of uncertain second-order nonlinear systems. By delicately introducing extra manipulations in the feedback domination and revamping the technique of adding a power integrator, a new approach is developed, by which a state feedback controller, together with a suitable Lyapunov function, which is critical for verifying fixed-time convergence, can be explicitly organized to render the closed-loop system fixed-time stable. The major novelty of this paper is attributed to a subtle strategy that offers a distinct perspective in controller design as well as stability analysis in the problem of fixed-time stabilization for nonlinear systems. Finally, the proposed approach is applied to the attitude stabilization of a spacecraft to demonstrate its merits and effectiveness.

Method of an Asymptotic Analysis of the Nonlinear Monotonic Stability of the Oscillation at the Problem of Damping of the Angle of Attack of a Symmetric Spacecraft

“…Note, that in [19] the problem of stabilization with a fixed time was considered for a class of the indefinite nonlinear systems of the second order. At the same time, a new approach has been developed that can be used to obtain a feedback controller, together with the corresponding Lyapunov function.…”