We provide novel reduced-order observer designs for continuous-time nonlinear systems with measurement error. Our first result applies to systems with continuous output measurements, and provides observers that converge in a fixed finite time that is independent of the initial state when the measurement error is zero. Our second result applies under discrete measurements, and provides observers that converge asymptotically with a rate of convergence that is proportional to the negative of the logarithm of the size of a sampling interval. Our observers satisfy an enhanced input-to-state stability property with respect to the measurement error, in which an overshoot term only depends on a recent history of the measurement error. We illustrate our observers using a model of a single-link robotic manipulator coupled to a DC motor with a nonrigid joint, and in a pendulum example.

我们为具有测量误差的连续时间非线性系统提供了新颖的降阶观测器设计。我们的第一个结果适用于具有连续输出测量的系统，并为观察者提供了在固定的有限时间内收敛的方法，该时间与测量误差为零时的初始状态无关。我们的第二个结果适用于离散测量，并且为观察者提供渐近收敛的收敛速度，该收敛速度与采样间隔大小的对数的负数成比例。我们的观察者在测量误差方面满足了增强的输入到状态稳定性属性，其中过冲项仅取决于测量误差的最新历史记录。我们用单链机器人操纵器模型耦合到具有非刚性接头的直流电动机模型来说明我们的观察者，