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

Abstract : 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.