Stability of Sampled-Data Control for Lurie Systems with Slope-Restricted Nonlinearities

Mathias  Giordani Titton; João Manoel  Gomes da Silva Jr.; Giórgio  Valmórbida

doi:10.48011/asba.v2i1.1661

Mathias Giordani Titton Universidade Federal do Rio Grande do Sul
João Manoel Gomes da Silva Jr. Universidade Federal do Rio Grande do Sul
Giórgio Valmórbida Université Paris-Saclay

DOI: https://doi.org/10.48011/asba.v2i1.1661

Keywords: Sampled-data control, Lurie systems, Stability analysis, Sector bounded nonlinearities, Looped-functional approach

Abstract

This paper deals with the stability analysis of aperiodic sampled-data Lurie systems, 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 whose derivative is negative along the trajectories of the continuous-time system. In addition, it contains a generalized Lurie-type function that is quadratic on both the states and the nonlinearity and has a Lurie-Postnikov integral term, which provides some advantages in comparison to simpler candidate functions. On this basis, stability conditions in the form of linear matrix inequalities (LMIs) are formulated. It is shown that the proposed conditions guarantee that the Lurie function is strictly decreasing at the sampling instants, which also implies that the continuous-time trajectories converge asymptotically to the origin. We then formulate some optimization problems for computing the
maximal intersampling interval or the maximal sector bounds for which the stability of the sampled-data closed-loop system is guaranteed. A numerical example to illustrate the results is provided.