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Construction Algorithm of Grassmann Space Parameters in Linear Output Feedback Systems  

Kim Su-Woon (Department of Electrical and Electronic Engineering, Cheju National University)
Publication Information
International Journal of Control, Automation, and Systems / v.3, no.3, 2005 , pp. 430-443 More about this Journal
Abstract
A general construction algorithm of the Grassmann space parameters in linear systems - so-called, the Plucker matrix, 'L' in m-input, p-output, n-th order static output feedback systems and the Plucker matrix, $ in augmented (m+d)-input, (p+d)-output, (n+d)-th order static output feedback systems - is presented for numerical checking of necessary conditions of complete static and complete minimum d-th order dynamic output feedback pole-assignments, respectively, and also for discernment of deterministic computation condition of their pole-assignable real solutions. Through the construction of L, it is shown that certain generically pole-assignable strictly proper mp > n system is actually none pole-assignable over any (real and complex) output feedbacks, by intrinsic rank deficiency of some submatrix of L. And it is also concretely illustrated that this none pole-assignable mp > n system by static output feedback can be arbitrary pole-assignable system via minimum d-th order dynamic output feedback, which is constructed by deterministic computation under full­rank of some submatrix of $L^{aug}$.
Keywords
Grassmann space; Plucker matrix in static output feedback system; some submatrix of Plucker matrix; complete/generic output feedback pole-assignment; deterministic computation condition of real solutions;
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