论文标题
Luenberger观察员用于离散时间非线性系统
Luenberger observers for discrete-time nonlinear systems
论文作者
论文摘要
在本文中，我们考虑了在卢恩伯格（Luenberger）最初的想法之后，在离散时间内设计渐近观察者的问题。这种方法是两步设计程序。第一步，问题是估计国家的函数。状态估计是通过反转该映射获得的。与连续的时间上下文类似，我们表明，如果引入了由输出的线性和稳定的离散时间系统，则始终可能会出现第一步。基于一个弱的可观察性假设，可以表明选择稳定的辅助系统的维度足够大，状态的估计功能是可逆的。在多项式输出的线性系统上说明了这种方法。还研究了与连续时间案例中获得的Luenberger观察者的联系。
In this paper, we consider the problem of designing an asymptotic observer for a nonlin-ear dynamical system in discrete-time following Luenberger's original idea. This approach is a two-step design procedure. In a first step, the problem is to estimate a function of the state. The state estimation is obtained by inverting this mapping. Similarly to the continuous-time context, we show that the first step is always possible provided a linear and stable discrete-time system fed by the output is introduced. Based on a weak observ-ability assumption, it is shown that picking the dimension of the stable auxiliary system sufficiently large, the estimated function of the state is invertible. This approach is illustrated on linear systems with polynomial output. The link with the Luenberger observer obtained in the continuous-time case is also investigated.
