A new robust observer design based discrete sliding mode control for time-varying delay systems with Hölder nonlinearities and unmatched disturbances

Sonia Ghrab , Sofiane Ahmed Ali (1) , Nicolas Langlois (1) , Hassani Messaoud (2)

1 Pôle Automatique et Systèmes
2 ENIM - École Nationale d’Ingénieurs de Monastir

In this paper, a new robust observer based sliding mode control approach is proposed for uncertain linear discrete-time delay system. The system under study is subject to time-varying states delay, and to different types of disturbances such as unmatched Unknown but norm-Bounded (UBB) parametric uncertainties and external disturbances. Additional nonlinearities have been considered as well. Such system nonlinearities are supposed to verify a Hölder condition of order α. A new delay-dependent sufficient conditions ensuring the robust asymptotic stability of the closed-loop system is derived in terms of Linear Matrix Inequalities (LMI). With regards to these conditions and considering the novel sliding surface-based observer, a new discrete-time sliding mode control law is designed. Finally, an illustrative example is exhibited to show the validity of the proposed control scheme.

Keywords: Observer-based Discrete-Time Sliding Mode Control; time-varying delay; Hölder nonlinearities; robustness

Domains: Engineering Sciences [physics]; Automatic

Sonia Ghrab, Sofiane Ahmed Ali, Nicolas Langlois, Hassani Messaoud. A new robust observer design based discrete sliding mode control for time-varying delay systems with Hölder nonlinearities and unmatched disturbances. 15th European Conference on Advanced Control and Diagnosis ACD'19, Nov 2019, Bologna, Italy. ⟨hal-02408072⟩