Wirtinger's inequality and Lyapunov-based sampled-data stabilization

Kun Liu; Emilia Fridman

doi:10.1016/j.automatica.2011.09.029

Wirtinger's inequality and Lyapunov-based sampled-data stabilization

Kun Liu, Emilia Fridman

School of Electrical Engineering

Tel Aviv University

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

Abstract

Discontinuous Lyapunov functionals appeared to be very efficient for sampled-data systems (Fridman, 2010; Naghshtabrizi, Hespanha, & Teel, 2008). In the present paper, new discontinuous Lyapunov functionals are introduced for sampled-data control in the presence of a constant input delay. The construction of these functionals is based on the vector extension of Wirtinger's inequality. These functionals lead to simplified and efficient stability conditions in terms of Linear Matrix Inequalities (LMIs). The new stability analysis is applied to sampled-data state-feedback stabilization and to a novel sampled-data static output-feedback problem, where the delayed measurements are used for stabilization.

Original language	English
Pages (from-to)	102-108
Number of pages	7
Journal	Automatica
Volume	48
Issue number	1
DOIs	https://doi.org/10.1016/j.automatica.2011.09.029
State	Published - Jan 2012

Keywords

LMI
LyapunovKrasovskii functional
Sampled-data systems
Time-delay

All Science Journal Classification (ASJC) codes

Control and Systems Engineering
Electrical and Electronic Engineering

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10.1016/j.automatica.2011.09.029

Cite this

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title = "Wirtinger's inequality and Lyapunov-based sampled-data stabilization",

abstract = "Discontinuous Lyapunov functionals appeared to be very efficient for sampled-data systems (Fridman, 2010; Naghshtabrizi, Hespanha, \& Teel, 2008). In the present paper, new discontinuous Lyapunov functionals are introduced for sampled-data control in the presence of a constant input delay. The construction of these functionals is based on the vector extension of Wirtinger's inequality. These functionals lead to simplified and efficient stability conditions in terms of Linear Matrix Inequalities (LMIs). The new stability analysis is applied to sampled-data state-feedback stabilization and to a novel sampled-data static output-feedback problem, where the delayed measurements are used for stabilization.",

keywords = "LMI, LyapunovKrasovskii functional, Sampled-data systems, Time-delay",

author = "Kun Liu and Emilia Fridman",

note = "Funding Information: This work was partially supported by Israel Science Foundation (grant No 754/10 ), and by China Scholarship Council . The material in this paper was not presented at any conference. This paper was recommended for publication in revised form by Associate Editor Tongwen Chen under the direction of Editor Ian R. Petersen.",

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N2 - Discontinuous Lyapunov functionals appeared to be very efficient for sampled-data systems (Fridman, 2010; Naghshtabrizi, Hespanha, & Teel, 2008). In the present paper, new discontinuous Lyapunov functionals are introduced for sampled-data control in the presence of a constant input delay. The construction of these functionals is based on the vector extension of Wirtinger's inequality. These functionals lead to simplified and efficient stability conditions in terms of Linear Matrix Inequalities (LMIs). The new stability analysis is applied to sampled-data state-feedback stabilization and to a novel sampled-data static output-feedback problem, where the delayed measurements are used for stabilization.

AB - Discontinuous Lyapunov functionals appeared to be very efficient for sampled-data systems (Fridman, 2010; Naghshtabrizi, Hespanha, & Teel, 2008). In the present paper, new discontinuous Lyapunov functionals are introduced for sampled-data control in the presence of a constant input delay. The construction of these functionals is based on the vector extension of Wirtinger's inequality. These functionals lead to simplified and efficient stability conditions in terms of Linear Matrix Inequalities (LMIs). The new stability analysis is applied to sampled-data state-feedback stabilization and to a novel sampled-data static output-feedback problem, where the delayed measurements are used for stabilization.

KW - LMI

KW - LyapunovKrasovskii functional

KW - Sampled-data systems

KW - Time-delay

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U2 - 10.1016/j.automatica.2011.09.029

DO - 10.1016/j.automatica.2011.09.029

M3 - مقالة

SN - 0005-1098

VL - 48

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EP - 108

JO - Automatica

JF - Automatica

IS - 1

ER -

Wirtinger's inequality and Lyapunov-based sampled-data stabilization

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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