Geodesic
A new LMI-based robust finite-time sliding mode control strategy for a class of uncertain nonlinear systems
Kybernetika, Tome 51 (2015) no. 6, pp. 1035-1048.

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This paper presents a novel sliding mode controller for a class of uncertain nonlinear systems. Based on Lyapunov stability theorem and linear matrix inequality technique, a sufficient condition is derived to guarantee the global asymptotical stability of the error dynamics and a linear sliding surface is existed depending on state errors. A new reaching control law is designed to satisfy the presence of the sliding mode around the linear surface in the finite time, and its parameters are obtained in the form of LMI. This proposed method is utilized to achieve a controller capable of drawing the states onto the switching surface and sustain the switching motion. The advantage of the suggested technique is that the control scheme is independent of the order of systems model and then, it is fairly simple. Therefore, there is no complexity in the utilization of this scheme. Simulation results are provided to illustrate the effectiveness of the proposed scheme.
DOI : 10.14736/kyb-2015-6-1035
Classification : 35F20, 37N35, 93C10, 93D09
Keywords: robust tracking; finite-time control; sliding mode control; nonlinear system; LMI; uncertainties 
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     author = {Mobayen, Saleh and Tchier, Fairouz},
     title = {A new {LMI-based} robust finite-time sliding mode control strategy for a class of uncertain nonlinear systems},
     journal = {Kybernetika},
     pages = {1035--1048},
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Mobayen, Saleh; Tchier, Fairouz. A new LMI-based robust finite-time sliding mode control strategy for a class of uncertain nonlinear systems. Kybernetika, Tome 51 (2015) no. 6, pp. 1035-1048. doi : 10.14736/kyb-2015-6-1035. http://geodesic.mathdoc.fr/articles/10.14736/kyb-2015-6-1035/

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