Despite the recent development of prescribed-time control theory, the highly desirable separation principle remains unavailable for nonlinear systems with only the output being measurable. In this paper, for the first time we establish such separation principle for a class of nonlinear systems, such that the prescribed-time observer and prescribed-time controller can be designed independently, and the parameter designs do not affect each other. Our method makes use of two parametric Lyapunov equations (PLEs) to generate two symmetric positive-definite matrices, aiming to avoid conservative treatments of nonlinear functions commonly associated with high-gain methods during the design process. Our work provides a stronger version of the matrix pencil formulation that is applicable when nonlinearities satisfy the so-called linear growth condition, even if the growth rate is unknown. In our method the selection of design parameters is straightforward as it involves only three parameters: one for the prescribed convergence time tf, and the other two are for the controller and the observer respectively, and the choice of the latter two parameters does not affect each other. Once the system order is determined, one can directly obtain reasonable ranges for these two parameters. Numerical simulations verify the effectiveness of the proposed method.

中文翻译：

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一类非线性系统的规定时间稳定的分离原理


尽管最近发展了规定时间控制理论，但非常理想的分离原理仍然不适用于非线性系统，只有输出是可测量的。在本文中，我们首次为一类非线性系统建立了这样的分离原理，使得规定时间的观察者和规定时间的控制器可以独立设计，参数设计之间没有相互影响。我们的方法利用两个参数 Lyapunov 方程 （PLE） 生成两个对称的正定矩阵，旨在避免在设计过程中对高增益方法通常相关的非线性函数进行保守处理。我们的工作提供了一个更强大的矩阵铅笔公式版本，当非线性满足所谓的线性生长条件时，即使生长速率未知，也适用。在我们的方法中，设计参数的选择很简单，因为它只涉及三个参数：一个是规定的收敛时间 tf，另外两个分别是控制器和观察器，后两个参数的选择互不影响。一旦确定了系统阶次，就可以直接获得这两个参数的合理范围。数值仿真验证了所提方法的有效性。