Linear hybrid systems with time-varying delays: H∞ stabilisation schemes

Magdi S. Mahmoud

doi:10.1504/IJSCC.2008.021119

Linear hybrid systems with time-varying delays: H_∞ stabilisation schemes

Magdi S. Mahmoud

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

In this paper, we provide new stabilisation schemes for a class of linear Hybrid Time-Delay (HTD) systems under arbitrary switching. These schemes are delay-independent and delay-dependent H_∞ stabilisation based on Propotional-Integral-Derivative (PID) feedback strategy. By adopting a selective Lyapunov-Krasovskii Functional (LKF), new criteria are constructed in a systematic way in terms of feasibility-testing of Linear Matrix Inequalities (LMIs). When the time-delay is a continuous bounded function, we derive the solution for nominal and polytopic models as well identifying several existing results as special cases. In case the time-delay is a differentiable time-varying function satisfying some bounding relations, we establish new parametrised LMI characterisations for PID feedback stabilisation. Numerical examples are provided to illustrate the theoretical developments.

Original language	English
Pages (from-to)	147-169
Number of pages	23
Journal	International Journal of Systems, Control and Communications
Volume	1
Issue number	2
DOIs	https://doi.org/10.1504/IJSCC.2008.021119
State	Published - 2008

Keywords

H stabilisation
LMIs, linear matrix inequalities
PID
hybrid systems
propotional-integral- derivative feedback
time-delay systems

ASJC Scopus subject areas

Control and Systems Engineering

Access to Document

10.1504/IJSCC.2008.021119

Cite this

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title = "Linear hybrid systems with time-varying delays: H∞ stabilisation schemes",

abstract = "In this paper, we provide new stabilisation schemes for a class of linear Hybrid Time-Delay (HTD) systems under arbitrary switching. These schemes are delay-independent and delay-dependent H∞ stabilisation based on Propotional-Integral-Derivative (PID) feedback strategy. By adopting a selective Lyapunov-Krasovskii Functional (LKF), new criteria are constructed in a systematic way in terms of feasibility-testing of Linear Matrix Inequalities (LMIs). When the time-delay is a continuous bounded function, we derive the solution for nominal and polytopic models as well identifying several existing results as special cases. In case the time-delay is a differentiable time-varying function satisfying some bounding relations, we establish new parametrised LMI characterisations for PID feedback stabilisation. Numerical examples are provided to illustrate the theoretical developments.",

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AB - In this paper, we provide new stabilisation schemes for a class of linear Hybrid Time-Delay (HTD) systems under arbitrary switching. These schemes are delay-independent and delay-dependent H∞ stabilisation based on Propotional-Integral-Derivative (PID) feedback strategy. By adopting a selective Lyapunov-Krasovskii Functional (LKF), new criteria are constructed in a systematic way in terms of feasibility-testing of Linear Matrix Inequalities (LMIs). When the time-delay is a continuous bounded function, we derive the solution for nominal and polytopic models as well identifying several existing results as special cases. In case the time-delay is a differentiable time-varying function satisfying some bounding relations, we establish new parametrised LMI characterisations for PID feedback stabilisation. Numerical examples are provided to illustrate the theoretical developments.

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KW - propotional-integral- derivative feedback

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