The problem of transforming a single-input single-output nonlinear discrete-time state equations into the extended observer form is studied in this paper. Unlike previous solutions which compute the injection terms from the input–output equations, in this paper the computations utilize directly the given state equations. An algorithm is given to find step-by-step the necessary transformation by computing backward-shifts of functions computed in previous step. It is shown that the integrability conditions presented in the algorithm are necessary and sufficient for solvability of the problem. Various examples have been studied to demonstrate the usefulness of the algorithm.

中文翻译：

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离散时间状态方程转化为扩展观测器形式的算法

研究了单输入单输出非线性离散时间状态方程转化为扩展观测器形式的问题。与之前根据输入输出方程计算注入项的解决方案不同，本文的计算直接利用给定的状态方程。给出了一种算法，通过计算上一步计算的函数的后移来逐步找到必要的变换。结果表明，算法中给出的可积条件对于问题的可解性是必要且充分的。已经研究了各种示例来证明该算法的有用性。