Prescribed-Time Stabilization of a Class of Nonlinear Systems by Linear Time-Varying Feedback

• Published in: IEEE transactions on automatic control Vol. 66; no. 12; pp. 6123 - 6130
• Main Authors: Zhou, Bin, Shi, Yang
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.12.2021; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Closed loop systems; Finite-time stabilization; global stabilization; linear feedback; Linear feedback control systems; Nonlinear systems; Output feedback; prescribed-time stabilization; Stabilization; State feedback; Time-varying systems
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2021.3061645

This article studies the problem of prescribed-time global stabilization of a class of nonlinear systems, where the nonlinear functions are unknown but satisfy a linear growth condition. By using solutions to a class of parametric Lyapunov equations containing a time-varying parameter that goes to infinity as the time approaches the prescribed settling time, linear time-varying feedback is designed explicitly to solve the considered problem, with the help of a Lyapunov-like function. It is shown moreover that the control signal is uniformly bounded by a constant depending on the initial condition. Both linear state feedback and linear observer-based output feedback are considered. The effectiveness of the proposed approach is illustrated by a numerical example borrowed from the literature.