一类未知输入系统的降维观测器设计

在观测器匹配条件不满足的情况下, 针对一类线性时不变系统，探讨了一种降维观测器设计的问题.基于输出对未知输入相关度的概念，构造辅助输出，使得匹配条件得以满足.在假设辅助输出可测时提出了一种降维观测器的设计方法.实际上，辅助输出不完全可测，使用高增益观测器观测的辅助输出估计值代替辅助输出设计降维观测器.状态估计误差在特定的封闭球体内最终一致有界，通过改变观测器参数可以调节封闭球体的半径.对一个五阶系统设计降维观测器，仿真结果表明, 降维观测器和滑模观测器具有同样良好的观测效果.

Reduced-Order Observer Design for Systems with Unknown Inputs

This paper is concerned with the problem of estimating the states for a kind of linear systems unknown inputs when the so-called matching condition was not satisfied. Employing the concept of the relative degree of the system, the auxiliary output vector which may satisfy the observer matching condition was constructed. Based on the auxiliary output vector, a reduced-order observer approach was proposed. The high-gain observers were used to estimate auxiliary output vector. Then, instead of auxiliary output vector, by employing its estimation, a reduced-order observer was constructed. The state estimation error is shown to be uniformly and ultimately bounded with respect to a ball whose radius can be adjusted by design parameters. The design method was declared and carried out with an illustrative example of a five order model. The comparison between estimation performance of the sliding observer and reduced-order observer shows that the latter has the same good performance as the former.