基于循环子空间理论的线性系统测试矩阵优化

研究了线性定常系统在循环指数大于1(即其约当标准形不同的约当块有重根)的情况下测试矩阵的优化方法.以循环子空间相关定理的证明为基础,根据根向量链的相关特性,得到了测试向量的线性和与系统观测性的直接关系,给出了在保证系统可观测性的同时,使得测试代价最小的测试矩阵优化方法.算例表明,提出的方法简单直观,对配置测试向量具有良好的工程价值.

Measurement Matrix Optimization for Linear Systems Based on Cyclic Subspace Theory

A measurement matrix optimization approach for the linear time-invariant system of which the cyclic index is bigger than 1(some different Jordan blocks of its Jordan canonical form have the same eigenvalue) was studied.Based on the proving of some cyclic subspace theories and relative properties of root vector chain,the relationship of measurement vectors' linear combination and the system observability was obtained.An approach which can achieve the minimum test cost and assure the system observability at t...