Tube-Based Model Predictive Control for Linear Discrete Time Systems with State Delay and Bounded Disturbances

This paper proposes a tube-based model predictive control algorithm for linear discrete time systems with state delay and bounded disturbances to ensure input-to-state stability. Firstly, we solve an optimization problem with delayed parameters to obtain a nominal control law. Then, we design a discrete time Lyapunov-Krasovskii function to derive an ancillary control law. Combining the two control laws, we obtain a control law that can ensure the system is input-to-state stable. Next, input-to-state stability is proved by a Lyapunov method. Moreover, the feasibility of the control algorithm is ensured by introducing constraints about the control laws in delayed time interval into the system. Finally, the effectiveness of the developed control strategy is verified by simulations.