The state estimation problem of a class of nonlinear singularly perturbed systems with discrete measurements is investigated. The fast dynamics is assumed to be linear and exponentially stable. Under this assumption and some additional conditions, an asymptotic representation of the fast state is obtained in terms of the slow state and the known input. Then the full state estimation problem reduces to the slow state estimation problem. Based on this observation, an impulsive observer based estimation scheme is presented in the framework of singular perturbation. The continuous part of the proposed impulsive observer is a copy of the reduced-order slow dynamics of the observed system, while the impulse part is responsible for the implementation of the sample-triggered update of the observer state whenever a new sample of the output arrives. The estimation error is analyzed via a discontinuous Lyapunov function, and an $\epsilon$-independent observer gain is designed. It is shown that the resulting estimation error exponentially converges towards an ultimate bound of order $O\left(\epsilon \right)$. The theoretical results are successfully applied to state estimates of Chua’s circuit and a flexible link robot. The simulation results demonstrate that the proposed state estimation scheme can achieve a desirable estimation accuracy for small enough $\epsilon >0$.

研究了一类具有离散测量的非线性奇异摄动系统的状态估计问题。快速动力学被认为是线性的并且是指数稳定的。在此假设和一些其他条件下，就慢速状态和已知输入而言，获得了快速状态的渐近表示。然后，全状态估计问题简化为慢状态估计问题。基于这种观察，在奇异摄动框架下提出了一种基于脉冲观测器的估计方案。提议的脉冲观测器的连续部分是被观测系统的降阶慢动力学的副本，而脉冲部分负责在输出的新样本到来时实现观察者状态的样本触发更新。 。$\epsilon$-独立的观察者增益被设计。结果表明，所得的估计误差以指数形式收敛到阶的极限$Ø（\epsilon ）$。理论结果已成功地应用于蔡氏电路和柔性链接机器人的状态估计。仿真结果表明，所提出的状态估计方案可以在较小的情况下达到理想的估计精度。$\epsilon >0$。