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

In this paper, we design a new robust Observer-based Discrete-Time Sliding Mode Control for an uncertain linear discrete-time delay system. The considered system is subject to time-varying states delay, unmatched Unknown and norm-Bounded UBB parametric uncertainties, external disturbances and nonlinearities which are assumed to satisfy a Hölder condition. A new delay-dependent sufficient conditions guaranteeing the robust asymptotic stability of the closed-loop system is derived in terms of Linear Matrix Inequalities. With respect to these conditions, a new discrete-time sliding mode control law is designed based on a novel observer structure and a new sliding surface. A numerical example is presented to illustrate the efficiency of our proposed approach.