H∞-Sliding mode control of one-sided Lipschitz nonlinear systems subject to input nonlinearities and polytopic uncertainties

Wajdi Saad; Anis Sellami; Germain Garcia

doi:10.1016/j.isatra.2018.12.040

H_∞-Sliding mode control of one-sided Lipschitz nonlinear systems subject to input nonlinearities and polytopic uncertainties

ISA Trans. 2019 Jul:90:19-29. doi: 10.1016/j.isatra.2018.12.040. Epub 2019 Jan 25.

Authors

Wajdi Saad¹, Anis Sellami², Germain Garcia³

Affiliations

¹ LISIER, National High School of Engineers of Tunis ENSIT, University of Tunis, 5 Av. Taha Hussein, Tunis, Tunisia. Electronic address: wajdi.saad@esstt.rnu.tn.
² LISIER, National High School of Engineers of Tunis ENSIT, University of Tunis, 5 Av. Taha Hussein, Tunis, Tunisia. Electronic address: anis.sellami@esstt.rnu.tn.
³ Research Laboratory LAAS-CNRS, University of Toulouse, Av. Colonel Roche F-31400, Toulouse, France. Electronic address: garcia@laas.fr.

PMID: 30718045
DOI: 10.1016/j.isatra.2018.12.040

Abstract

This paper is concerned with the control problem for different types of one-sided Lipschitz (OSL) nonlinear systems subject to input nonlinearities, unmatched polytopic uncertainties and external perturbations. The design framework gathers the high robustness qualities of the sliding mode control (SMC) and the H_∞ technique. The aims is to consider the bounded L₂ disturbance attenuation measure in the analysis of sliding mode dynamics, thus to ameliorate the performance of the SMC system. An integral switching surface function is chosen and related synthesis conditions for the sliding mode dynamics are formulated in terms of linear matrix inequalities (LMIs). Then, an appropriate control law is synthesized such that reachability of the switching manifold is ensured. At last, simulation examples are provided to prove the feasibility of the proposed approach.

Keywords: Nonlinear input; One-sided Lipschitz; Poly-quadratic stability; Sliding mode control.