带输入延时的连续时间系统的离散化

含多项式插值的Runge-Kutta方法应用于对带输入延时的连续时间系统的离散化中. 与传统的离散化方法相比, 本文提出的方法是有效且精度高阶的. 此方法的精度与Runge-Kutta法及插值多项式的精度紧密相关. 本文讨论了离散化方法的近似精度阶及最大可达的精度阶. 除此之外, 也分析了方法的输入状态稳定性. 为保证相应离散系统的稳定性, 可通过考察RK法的绝对稳定域来选择采样时间. 特别当RK法是A-稳定时, 可以不受稳定性的约束选择采样时间. 最后提供了一个数值例子来证明方法的优越性.

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.