This work proposes a design scheme for arbitrary order discrete-time sliding mode observers for input-affine nonlinear systems. The dynamics of the estimation errors are represented in a pseudo-linear form, where the coefficients of the characteristic polynomial comprise the nonlinearities of the algorithm. The design process is reduced to a state-dependent eigenvalue placement procedure. Moreover, two different discrete-time eigenvalue mappings are proposed. As basis for the eigenvalue mappings serves a modified version of the continuous-time uniform robust exact differentiator. Due on the chosen eigenvalue mapping the proposed algorithm does not suffer from discretization chattering. Global asymptotic stability of the estimation errors for observers of order 2 and 3 is proven and the method to prove stability for higher order observers is demonstrated. The performance of a 3-rd order observer is illustrated in simulation. Simulation studies indicate that proposed discrete-time observer might possess an upper bound of its convergence time independent of the initial conditions.

这项工作提出了一种用于输入仿射非线性系统的任意阶离散时间滑模观测器的设计方案。估计误差的动态以伪线性形式表示，其中特征多项式的系数包括算法的非线性。设计过程被简化为依赖于状态的特征值放置过程。此外，提出了两种不同的离散时间特征值映射。作为特征值映射的基础，服务于连续时间统一鲁棒精确微分器的修改版本。由于所选择的特征值映射，所提出的算法不会受到离散化抖动的影响。证明了二阶和三阶观察者估计误差的全局渐近稳定性，并证明了证明高阶观察者稳定性的方法。三阶观测器的性能在仿真中得到了说明。模拟研究表明，所提出的离散时间观测器可能拥有独立于初始条件的收敛时间上限。