Semi-global exact prescribed-time stabilization of linear systems by bounded linear time-varying feedback
Abstract
This paper addresses the problem of semi-global exact prescribed-time stabilization of linear systems by bounded controls. To solve such a problem, one needs to construct a parameterized quadratic control Lyapunov function whose corresponding level set can be made arbitrarily large (for achieving semi-global stabilization) and such that the real parts of the poles of the closed-loop system approach minus infinity as the parameter approaches infinity (for achieving prescribed-time stabilization). This objective is achieved by proposing a nested parametric Lyapunov equation (PLE)-based approach, through which only two linear matrix equations need to be solved in the controller design stage without using real-time state information. Under the proposed structural condition, the nested PLE-based approach guarantees semi-global exact prescribed-time stabilization for any prescribed bounded set of initial conditions, provided that the prescribed settling time is sufficiently large. A numerical example is provided to demonstrate the effectiveness of the designed controller.
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BibTeX
@misc{xie2026semiglobal,
title = {{Semi-global exact prescribed-time stabilization of linear systems by bounded linear time-varying feedback}},
author = {Qinyu Xie and Bin Zhou},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.07281},
eprint = {2609.07281},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.07281},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Semi-global exact prescribed-time stabilization of linear systems by bounded linear time-varying feedback
AU - Qinyu Xie
AU - Bin Zhou
PY - 2026
DA - 2026/09/07
PB - arXiv
DO - 10.48550/arxiv.2609.07281
UR - https://arxiv.org/abs/2609.07281
AB - This paper addresses the problem of semi-global exact prescribed-time stabilization of linear systems by bounded controls. To solve such a problem, one needs to construct a parameterized quadratic control Lyapunov function whose corresponding level set can be made arbitrarily large (for achieving semi-global stabilization) and such that the real parts of the poles of the closed-loop system approach minus infinity as the parameter approaches infinity (for achieving prescribed-time stabilization). This objective is achieved by proposing a nested parametric Lyapunov equation (PLE)-based approach, through which only two linear matrix equations need to be solved in the controller design stage without using real-time state information. Under the proposed structural condition, the nested PLE-based approach guarantees semi-global exact prescribed-time stabilization for any prescribed bounded set of initial conditions, provided that the prescribed settling time is sufficiently large. A numerical example is provided to demonstrate the effectiveness of the designed controller.
ER -