Switched discrete-time systems with time-varying delays: A generalized H2 approach

Magdi S. Mahmoud

doi:10.1016/j.camwa.2008.10.066

Switched discrete-time systems with time-varying delays: A generalized H₂ approach

Magdi S. Mahmoud^*

^*Corresponding author for this work

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

26 Scopus citations

Abstract

In this paper, we investigate the delay-dependent performance analysis and control synthesis of a class of linear discrete-time hybrid systems with time-varying delays. We employ hybrid Lyapunov-Krasovskii functionals to establish the desired results under arbitrary switching. A generalized H₂ approach is adopted and new parameterized linear matrix inequalities (LMIs) characterization are developed to guarantee the delay-dependent asymptotic stability. Design of generalized H₂ state feedback and dynamic output-feedback controllers are subsequently constructed. A numerical example is solved in detail to illustrate the theoretical developments.

Original language	English
Pages (from-to)	79-95
Number of pages	17
Journal	Computers and Mathematics with Applications
Volume	57
Issue number	1
DOIs	https://doi.org/10.1016/j.camwa.2008.10.066
State	Published - Jan 2009

Bibliographical note

Funding Information:
This research work is supported by KFUPM research project No. IN080404 .

Keywords

Delay-dependent stability
Hybrid Lyapunov-Krasovskii functional
Hybrid output-feedback
Hybrid state-feedback
Hybrid systems
LMIs

ASJC Scopus subject areas

Modeling and Simulation
Computational Theory and Mathematics
Computational Mathematics

Access to Document

10.1016/j.camwa.2008.10.066

Cite this

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title = "Switched discrete-time systems with time-varying delays: A generalized H2 approach",

abstract = "In this paper, we investigate the delay-dependent performance analysis and control synthesis of a class of linear discrete-time hybrid systems with time-varying delays. We employ hybrid Lyapunov-Krasovskii functionals to establish the desired results under arbitrary switching. A generalized H2 approach is adopted and new parameterized linear matrix inequalities (LMIs) characterization are developed to guarantee the delay-dependent asymptotic stability. Design of generalized H2 state feedback and dynamic output-feedback controllers are subsequently constructed. A numerical example is solved in detail to illustrate the theoretical developments.",

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AB - In this paper, we investigate the delay-dependent performance analysis and control synthesis of a class of linear discrete-time hybrid systems with time-varying delays. We employ hybrid Lyapunov-Krasovskii functionals to establish the desired results under arbitrary switching. A generalized H2 approach is adopted and new parameterized linear matrix inequalities (LMIs) characterization are developed to guarantee the delay-dependent asymptotic stability. Design of generalized H2 state feedback and dynamic output-feedback controllers are subsequently constructed. A numerical example is solved in detail to illustrate the theoretical developments.

KW - Delay-dependent stability

KW - Hybrid Lyapunov-Krasovskii functional

KW - Hybrid output-feedback

KW - Hybrid state-feedback

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