Stability analysis of Lure systems under aperiodic sampled-data control
Mathias Giordani Titton
PPGEE/DELAE, Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, Rio Grande do Sul, Brazil
Search for more papers by this authorCorresponding Author
João Manoel Gomes da Silva Jr.
PPGEE/DELAE, Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, Rio Grande do Sul, Brazil
Correspondence João Manoel Gomes da Silva Jr., PPGEE/DELAE, Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, Rio Grande do Sul, Brazil.
Email: [email protected]
Search for more papers by this authorGiorgio Valmorbida
Laboratoire des Signaux et Systèmes, CentraleSupélec, CNRS, Université Paris-Saclay, Project DISCO Inria-Saclay, Gif-sur-Yvette, France
Search for more papers by this authorMathias Giordani Titton
PPGEE/DELAE, Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, Rio Grande do Sul, Brazil
Search for more papers by this authorCorresponding Author
João Manoel Gomes da Silva Jr.
PPGEE/DELAE, Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, Rio Grande do Sul, Brazil
Correspondence João Manoel Gomes da Silva Jr., PPGEE/DELAE, Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, Rio Grande do Sul, Brazil.
Email: [email protected]
Search for more papers by this authorGiorgio Valmorbida
Laboratoire des Signaux et Systèmes, CentraleSupélec, CNRS, Université Paris-Saclay, Project DISCO Inria-Saclay, Gif-sur-Yvette, France
Search for more papers by this authorAbstract
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.
CONFLICT OF INTEREST STATEMENT
The authors declare that there is no conflict of interest for this article.
Open Research
DATA AVAILABILITY STATEMENT
Data available on request from the authors.
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