Prescribed-Time Stabilization of a Class of Nonlinear Systems by Linear Time-Varying Feedback
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 i...
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| Published in | IEEE transactions on automatic control Vol. 66; no. 12; pp. 6123 - 6130 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
New York
IEEE
01.12.2021
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0018-9286 1558-2523 |
| DOI | 10.1109/TAC.2021.3061645 |
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| Abstract | 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. |
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| AbstractList | 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. |
| Author | Zhou, Bin Shi, Yang |
| Author_xml | – sequence: 1 givenname: Bin orcidid: 0000-0003-1272-2652 surname: Zhou fullname: Zhou, Bin email: binzhou@hit.edu.cn organization: Center for Control Theory and Guidance Technology, Harbin Institute of Technology, Harbin, China – sequence: 2 givenname: Yang orcidid: 0000-0003-1337-5322 surname: Shi fullname: Shi, Yang email: yshi@uvic.ca organization: Department of Mechanical Engineering, University of Victoria, Victoria, BC, Canada |
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| SubjectTerms | 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 |
| Title | Prescribed-Time Stabilization of a Class of Nonlinear Systems by Linear Time-Varying Feedback |
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