Quantum mechanics

Control (management)

Linear system

Applied mathematics

Stability (learning theory)

Computer science

Bounded function

Physics

Nonlinear system

Mathematics

Lyapunov function

Mathematical analysis

Artificial intelligence

Control theory (sociology)

Machine learning

Automatica

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.

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