A Linear Time-Varying Inequality Approach for Prescribed Time Stability and Stabilization

This article studies the problem of finite-time, fixed-time, and prescribed-time stability analysis and stabilization. First, a linear time-varying (LTV) inequality-based approach is introduced for prescribed-time stability analysis. Then, it is shown that the existing nonlinear Lyapunov inequalities-based finite- and fixed-time stability criteria can be recast into the unified framework of the LTV inequality-based approach for prescribed-time stability. Finally, the unified LTV inequality-based approach is used to solve the global prescribed-time stabilization problem of the attitude control system of a rigid spacecraft with disturbance, and a bounded nonlinear time-varying controller is proposed via back stepping. Numerical simulations are presented to show the effectiveness of the proposed methods.