线性系统有限时间函数观测器设计的参数化方法

Parameterized design of finite time functional observer in linear systems

研究了线性系统有限时间函数观测器的参数化设计问题,其目的是通过设计参数化形式的函数观测器,使其在给定有限时间内能够直接估计关于线性系统状态的线性函数。基于一类Sylvester矩阵方程的参数化解,给出了该有限时间函数观测器所有增益矩阵的参数化表达式,其所含的自由参数为控制系统设计提供了全部的自由度,可通过适当选择这些自由参数使其满足某些系统性能指标。最后,数值例子及其仿真结果验证了所提线性系统有限时间函数观测器参数化设计方法的简单性和有效性。

A parameterized design problem of the finite time functional observers in the linear systems is investigated.The aim is to design the parameterized functional observers which can directly estimate the linear functions of the state of the linear systems within a predefined finite time.By using the parameterized solutions of a class of Sylvester matrix equations,the parameterized expressions of all the gain matrices in the finite time functional observer are presented.The free parameters of the proposed finite time functional observers can offer all the design degrees of freedom in control system design and can be selected to satisfy some system performance.Finally,a numerical example and its simulation results show the simplicity and effectiveness of the proposed parametric design method of the finite time functional observers in the linear systems.