Geometric Insight and Structure Algorithms for Unknown-State, Unknown-Input Reconstruction in Linear Multivariable Systems
Geometric Insight and Structure Algorithms for Unknown-State, Unknown-Input Reconstruction in Linear Multivariable Systems
复制标题
线性多变量系统中未知状态、未知输入重构的几何洞察和结构算法
DOI：
10.3182/20110828-6-it-1002.00152
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发表时间：
2011
期刊：
影响因子：
--
通讯作者：
D. Bernstein
中科院分区：
文献类型：
--
作者：
G. Marro;E. Zattoni;D. Bernstein
摘要讨论了一种动态系统综合的代数方法，该方法可重构具有未知初始状态的离散线性多变量系统的一般不可达输入。设计的方法利用几何性质的关键子空间的原始系统和代数性质的Moore-Penrose逆Toeplitz矩阵相关的算法计算这些子空间。非最小相位不变零考虑隐式与所提出的技术，而最小相位不变零需要在原始系统和重建器之间插入滤波器。该程序适用于严格适当或非严格适当的系统。
Abstract An algebraic approach to the synthesis of a dynamic system that reconstructs the generic inaccessible input of a discrete-time linear multivariable system with unknown initial state is discussed. The method devised exploits geometric properties of key subspaces for the original system and algebraic properties of the Moore-Penrose inverse of Toeplitz matrices related to the algorithms for computing those subspaces. Nonminimum-phase invariant zeros are taken into account implicitly with the proposed techniques, while minimum-phase invariant zeros require that a filter be inserted between the original system and the reconstructor. The procedure applies to either strictly-proper or non-strictly-proper systems.