Stability analysis of Lure systems under aperiodic sampled-data control

被引：3

作者：

Titton, Mathias Giordani ^{[1
]}

da Silva Jr, Joao Manoel Gomes ^{[1
]}

Valmorbida, Giorgio ^{[2
,3
]}

Jungers, Marc

机构：

[1] Univ Fed Rio Grande UFRGS, PPGEE, DELAE, Porto Alegre, RS, Brazil

[2] Univ Paris Saclay, Project DISCO Inria Saclay, Lab Signaux & Syst, Cent Supelec,CNRS, Gif Sur Yvette, France

[3] Univ Lorraine, CNRS, CRAN, Nancy, France

来源：

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL | 2023年 / 33卷 / 12期

关键词：

looped-functional approach; Lure systems; sampled-data control; sector bounded nonlinearities; stability analysis; ABSOLUTE STABILITY; NONLINEAR-SYSTEMS; LINEAR-SYSTEMS; STABILIZATION; SECTOR;

D O I：

10.1002/rnc.6744

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

This article deals with the stability analysis of Lure type systems through aperiodic sampled-data control laws, where the nonlinearity is assumed to be both sector and slope restricted. The proposed method is based on the use of a new class of looped-functionals, which depends on the nonlinearity and its slope, and on a generalized Lure type function, that is quadratic on both the states and the nonlinearity and has a Lure-Postnikov integral term. On this basis, conditions in the form of linear matrix inequalities to certify global or regional asymptotic stability of the closed-loop system are obtained. These conditions are then used in optimization problems for computing the maximum intersampling interval or the maximum sector bounds for which the stability of the sampled-data closed-loop system is guaranteed. Numerical examples to illustrate the results are provided.

引用

页码：7130 / 7153

页数：24

共 40 条

[1]

Astrom K. J., 2013, Computer-Controlled Systems: Theory and Design

[2] A LIFTING TECHNIQUE FOR LINEAR PERIODIC-SYSTEMS WITH APPLICATIONS TO SAMPLED-DATA CONTROL [J].

BAMIEH, B ;

PEARSON, JB ;

FRANCIS, BA ;

TANNENBAUM, A .

SYSTEMS & CONTROL LETTERS, 1991, 17 (02) :79-88

[3] Convergence and Equivalence Results for the Jensen's Inequality-Application to Time-Delay and Sampled-Data Systems [J].

Briat, Corentin .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2011, 56 (07) :1660-1665

[4] Zames-Falb multipliers for absolute stability: From O'Shea's contribution to convex searches [J].

Carrasco, Joaquin ;

Turner, Matthew C. ;

Heath, William P. .

EUROPEAN JOURNAL OF CONTROL, 2016, 28 :1-19

[5] Control design for a class of nonlinear continuous-time systems [J].

Castelan, Eugenio B. ;

Tarbouriech, Sophie ;

Queinnec, Isabelle .

AUTOMATICA, 2008, 44 (08) :2034-2039

[6] Robust sampled-data stabilization of linear systems: an input delay approach [J].

Fridman, E ;

Seuret, A ;

Richard, JP .

AUTOMATICA, 2004, 40 (08) :1441-1446

[7] A refined input delay approach to sampled-data control [J].

Fridman, Emilia .

AUTOMATICA, 2010, 46 (02) :421-427

[8] A Discrete-Time Approach to Stability Analysis of Systems With Aperiodic Sample-and-Hold Devices [J].

Fujioka, Hisaya .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2009, 54 (10) :2440-2445

[9] Sampled-data control of Lur'e systems [J].

Gabriel, Gabriela W. ;

Geromel, Jose C. .

NONLINEAR ANALYSIS-HYBRID SYSTEMS, 2021, 40

[10] Stability analysis of discrete-time Lur'e systems [J].

Gonzaga, Carlos A. C. ;

Jungers, Marc ;

Daafouz, Jamal .

AUTOMATICA, 2012, 48 (09) :2277-2283

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