Title: Lin-Sontag and common Lyapunov functions for stabilising control of a switched nonlinear systems

Authors: Abdessamad Abdelhedi; Wided Saadi; Driss Boutat; Lassaad Sbita

Addresses: Unit of Photovoltaic, Wind and Geothermal Systems, National Engineering School of Gabes, University of Gabes, Rue Omar Ibn-Elkhattab, Zrig, Gabès, 6029, Gabes, Tunisia ' Unit of Photovoltaic, Wind and Geothermal Systems, National Engineering School of Gabes, University of Gabes, Rue Omar Ibn-Elkhattab, Zrig, Gabès, 6029, Gabes, Tunisia ' INSA-Bourges, Laboratory PRISME, Loire Valley University, 88 Boulevard Lahitolle 18020, Bourges Cedex, France ' Unit of Photovoltaic, Wind and Geothermal Systems, National Engineering School of Gabes, University of Gabes, Rue Omar Ibn-Elkhattab, Zrig, Gabès, 6029, Gabes, Tunisia

Abstract: This work presents a control of switched nonlinear systems. The approach is based on stabilisation by using control Lyapunov functions. A necessary and sufficient condition for stabilisation based on the existence of a common Lyapunov control function for switching subsystems is presented for the first time. Secondly, a stabilisation control device is designed for nonlinear switching system using the theory of common Lyapunov function and state feedback control of Lin-Sontag. Finally, this proposed approach is illustrated on the example of a switched reactor.

Keywords: switched systems; stabilisation; control; Lyapunov functions; reactor.

DOI: 10.1504/IJISE.2018.095529

International Journal of Industrial and Systems Engineering, 2018 Vol.30 No.3, pp.316 - 328

Received: 15 Jul 2016
Accepted: 28 Oct 2016
Published online: 09 Oct 2018 *

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