摘要
最小阶线性函数观测器直接估测Kx(t)信号,其中K是任意给定的.这个观测器的极点在设计时也是任意给定的.1986年发表的一个设计程序所要解的公式是将这一设计问题简化成的一组线性方程组,保证设计出来的观测器阶数的上下限也是至今为止最低的.自1986年以来,上述的这一线性方程组已被宣称定性为这一设计问题的最可能简单的公式,上述的观测器阶数的上下限也已被宣称定性为最可能低的上下限.本文进一步证明和宣称定性这一1986年的结果是这一设计问题的最可能好的理论结果.这一宣称定性的重大意义可由以下两个事实来说明.首先这一明确而决定性的宣称定性是该结果发表26年后才作出的.其次相比最近发表的一篇相关论文,该文只是将整个设计问题推导成复杂得多的公式,没能提出真正系统地计算该复杂公式的解的计算程序,却宣称只有该文才得到了整个设计问题的解!
A design algorithm in 1986 for minimal order linear functional observers that estimate Kx（t） directly for arbitrarily given K and with arbitrarily given poles, is based on a simplified design formulation that is only a single set of linear equations, and guarantees observer order upper and lower bounds that are the lowest ever since. Since 1986, this single set of linear equations has been claimed the simplest possible formulation of the design problem, and this guaranteed observer order upper bound has been proved to be the lowest possible upper bound. This paper further claims that that result of 1986 is the best possible theoretical result of the design problem. This new claim is very significant due to two facts. Firstly, this new and clearcut claim for that result of 1986 has not been made for 26 years. Secondly, a recent paper which only reformulated the original design problem to be much more complicated, and which failed to provide a systematic algorithm that can compute the solution of its complicated reformulation, self-claimed the only solution to the design problem!
关键词
最小阶
线性函数观测器设计
矩阵方程组
Minimal order
linear functional observer design
matrix equations
