A new robust adaptive sliding mode control for MIMO uncertain discrete systems with unknown time varying state delay using a novel surface

In In this article, we propose a new robust adaptive sliding mode control method for discrete linear uncertain MIMO systems with variable and unknown state delay. In this work, the uncertainties are assumed to be unknown but bounded, with their bounds also being unknown. The idea is to integrate the estimation of the upper bounds of the uncertainties into the system control calculation. This new control law is based on the choice of the Lyapunov function. To evaluate the performance of the new control law, a comparative study with the method of [Ghrab, S., Ali, S. A., Benamor, A., Langlois, N., & Messaoud, H. (2024). A novel robust discrete-time integral sliding mode tracking control design for time-varying delay MIMO systems with unknown uncertainties. ISA Transactions, 145, 1–18. https: /doi.org/10.1016/j.isatra.2023.11.024.] was conducted. Subsequently, an application to a diesel engine was presented. The effectiveness of the new approach was demonstrated by the asymptotic stability of the system state components obtained and the reduction of their steady-state errors, the stability of the calculated control signal, and the reduced convergence time of the sliding surface to zero.