Discretization of Continuous-time Systems with Input Delays

In this paper, the Runge-Kutta (RK) method, which involves the polynomial interpolation is adopted to discretize continuous-time systems with input delay. The proposed scheme is an efficient and higher-order approach compared with conventional discretizing methods. The accuracy of the proposed conversion scheme is closely related to the order of RK as well as that of the polynomial interpolation. Both the approximate order and the maximal attainable order of the discretization are discussed. In addition, the input-to-state stability of the scheme is analyzed. In order to guarantee the stability of the corresponding discrete system, the sampling time can be chosen by investigating the absolute stability region of the RK method. Especially, when the RK method is A-stable, the sampling time can be selected without being constrained by stability considerations. A numerical experiment is provided to demonstrate the superior performance of the method.