article

Finite-Time Stability and Stabilization for Continuous Systems with Additive Time-Varying Delays

Authors:

Jun NieAuthors Info & Claims

Circuits, Systems, and Signal Processing, Volume 36, Issue 7

Pages 2971 - 2990

https://doi.org/10.1007/s00034-016-0443-z

Published: 01 July 2017 Publication History

Abstract

This paper is centered on the problem of delay-dependent finite-time stability and stabilization for a class of continuous system with additive time-varying delays. Firstly, based on a new Lyapunov---Krasovskii-like function (LKLF), which splits the whole delay interval into some proper subintervals, a set of delay-dependent finite-time stability conditions, guaranteeing that the state of the system does not exceed a given threshold in fixed time interval, are derived in form of linear matrix inequalities. In particular, to obtain a less conservative result, we take the LKLF as a whole to examine its positive definite which can slack the requirements for Lyapunov matrices and reduce the loss information when estimating the bound of the function. Further, based on the results of finite-time stability, sufficient conditions for the existence of a state feedback finite-time controller, guaranteeing finite-time stability of the closed-loop system, are obtained and can be solved by using some standard numerical packages. Finally, some numerical examples are provided to demonstrate the less conservative and the effectiveness of the proposed design approach.

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Cited By

Shahbazzadeh MSadati S(2022)Delay-Dependent Stabilization of Time-Delay Systems with Nonlinear PerturbationsCircuits, Systems, and Signal Processing10.1007/s00034-021-01810-w41:2(684-699)Online publication date: 1-Feb-2022
https://dl.acm.org/doi/10.1007/s00034-021-01810-w
Gholami HBinazadeh T(2019)Robust Finite-Time H? Controller Design for Uncertain One-Sided Lipschitz Systems with Time-Delay and Input Amplitude ConstraintsCircuits, Systems, and Signal Processing10.1007/s00034-018-01018-538:7(3020-3040)Online publication date: 20-Jul-2019
https://dl.acm.org/doi/10.1007/s00034-018-01018-5
Guo TWu BWang YWang X(2018)Delay-Dependent Robust Finite-Time $$H_{\infty }$$H? Control for Uncertain Large Delay Systems Based on a Switching MethodCircuits, Systems, and Signal Processing10.5555/3288801.328881237:11(4753-4772)Online publication date: 1-Nov-2018
https://dl.acm.org/doi/10.5555/3288801.3288812

Finite-Time Stability and Stabilization for Continuous Systems with Additive Time-Varying Delays
1. Computing methodologies
  1. Artificial intelligence
    1. Control methods
2. Mathematics of computing
  1. Mathematical analysis

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cover image Circuits, Systems, and Signal Processing

Circuits, Systems, and Signal Processing Volume 36, Issue 7

July 2017

412 pages

ISSN:0278-081X

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Copyright © Copyright © 2017 Springer Science+Business Media New York.

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Birkhauser Boston Inc.

United States

Publication History

Published: 01 July 2017

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Cited By

Shahbazzadeh MSadati S(2022)Delay-Dependent Stabilization of Time-Delay Systems with Nonlinear PerturbationsCircuits, Systems, and Signal Processing10.1007/s00034-021-01810-w41:2(684-699)Online publication date: 1-Feb-2022
https://dl.acm.org/doi/10.1007/s00034-021-01810-w
Gholami HBinazadeh T(2019)Robust Finite-Time H? Controller Design for Uncertain One-Sided Lipschitz Systems with Time-Delay and Input Amplitude ConstraintsCircuits, Systems, and Signal Processing10.1007/s00034-018-01018-538:7(3020-3040)Online publication date: 20-Jul-2019
https://dl.acm.org/doi/10.1007/s00034-018-01018-5
Guo TWu BWang YWang X(2018)Delay-Dependent Robust Finite-Time $$H_{\infty }$$H? Control for Uncertain Large Delay Systems Based on a Switching MethodCircuits, Systems, and Signal Processing10.5555/3288801.328881237:11(4753-4772)Online publication date: 1-Nov-2018
https://dl.acm.org/doi/10.5555/3288801.3288812

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