Finite-time stability analysis and stabilization by bounded linear time-varying feedback

This paper studies finite-time stability analysis and finite-time stabilization of linear systems by bounded linear time-varying feedback. On the one hand, (both local and global) finite-time stability of general nonlinear time-varying systems is investigated by the comparison principle and the notion of finite-time escaping functions. Some Lyapunov-like stability theorems are established. On the other hand, finite-time and prescribed-time stabilization of linear systems by bounded linear time-varying feedback are revisited based on the proposed finite-time stability theorems. Two classes of new time-varying high-gain functions are proposed to reduce the regulation time. Some connections of the proposed results to existing results on Lyapunov-inequality based finite-time stability analysis and nonlinear feedback based finite-time stabilization are revealed. The effectiveness of the proposed methods is illustrated by a numerical example.