Approximate pole placement by involution and vector decomposition

作者：Leventides John^*; Kollias Iraklis

来源：IMA Journal of Mathematical Control and Information, 2016, 33(3): 859-871.

DOI：10.1093/imamci/dnv007

• algebraic control theory
• feedback systems
• pole assignment

In this paper, we consider some new tools and results for the approximate pole placement problem. This problem is related to solving a least distance problem from the Grassmann variety. When this variety is defined by a single quadratic, it entails an additional structure for a related vector space equipped with an involution. This implies a canonical orthogonal decomposition of vectors as well as a solution of the least distance problem from the zero set of the involution. The problem of the least distance of a linear space from the zero set of the involution is reduced to a numerical range problem of a related matrix. This result has been applied to solve a multivariable approximate pole placement problem by constant output feedback to systems of 2-inputs, 2-outputs and n-states when the generic arbitrary pole assignability condition 4 > n is not valid.

• 出版日期2016-9