Paper Info
Title
Fixed-Time Stabilization of Linear Delay Systems by Smooth Periodic Delayed Feedback
Abstract
This article studies fixed-time stabilization (FxTS) of a general controllable linear system with an input delay <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\tau$</tex-math></inline-formula> . It is shown that such a problem is not solvable if the prescribed convergence time <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$T_{\tau }$</tex-math></inline-formula> is smaller than <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$2\tau$</tex-math></inline-formula> . For <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$T_{\tau }\geq 3\tau$</tex-math></inline-formula> , a solution based on linear periodic delayed feedback (PDF) without any distributed delay is established. For <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$T_{\tau }&gt;2\tau$</tex-math></inline-formula> , a solution based on linear predictor-based PDF containing a distributed delay is proposed. For both cases, the gains of the PDF can be chosen as continuous, continuously differentiable, and even smooth, in the sense of infinitely many times differentiable. If only an output signal is available for feedback, two classes of linear observers with periodic coefficients are designed, so that their states converge to the current and future states of the system at a prescribed finite time, respectively. With the observed current and future states, FxTS can also be achieved by using, respectively, the PDF and observer-based PDF. A linear periodic feedback (without delay) is also established to solve the FxTS problem of linear systems with both instantaneous and delayed controls, which cannot be stabilized by any constant instantaneous feedback in certain cases. Two numerical examples verify the effectiveness of the proposed approaches.
Year
DOI
Venue
2022
10.1109/TAC.2021.3051262
IEEE Transactions on Automatic Control
Keywords
DocType
Volume
Fixed-time stabilization (FxTS),input time-delay,linear time-varying feedback,periodic delayed feedback (PDF),prescribed finite-time stabilization
Journal
67
Issue
ISSN
Citations 
2
0018-9286
0
PageRank 
References 
Authors
0.34
15
3
Name
Order
Citations
PageRank
Bin Zhou1115082.46
Wim Michiels251377.24
Jie Chen3647124.78