# New results in pole assignment by real output feedback

Rosenthal, J (1992). New results in pole assignment by real output feedback. SIAM Journal on Control and Optimization, 30(1):203-211.

## Abstract

This paper considers the problem of tuning natural frequencies of a linear system by a memoryless controller. Using algebro-geometric methods it is shown how it is possible to improve current sufficiency conditions.The main result is an exact combinatorial characterization of the nilpotency index of the $\bmod 2$ cohomology ring of the real Grassmannian. Using this characterization, new sufficiency results for generic pole assignment for the linear system with $m$-inputs, $p$-outputs, and McMillan degree $n$ are given. Among other results it is shown that $2.25 \cdot \max (m,p) + \min (m,p) - 3 \geq n$ is a sufficient condition for generic real pole placement, provided $\min (m,p) \geq 4$. ©1992 Society for Industrial and Applied Mathematics

## Abstract

This paper considers the problem of tuning natural frequencies of a linear system by a memoryless controller. Using algebro-geometric methods it is shown how it is possible to improve current sufficiency conditions.The main result is an exact combinatorial characterization of the nilpotency index of the $\bmod 2$ cohomology ring of the real Grassmannian. Using this characterization, new sufficiency results for generic pole assignment for the linear system with $m$-inputs, $p$-outputs, and McMillan degree $n$ are given. Among other results it is shown that $2.25 \cdot \max (m,p) + \min (m,p) - 3 \geq n$ is a sufficient condition for generic real pole placement, provided $\min (m,p) \geq 4$. ©1992 Society for Industrial and Applied Mathematics

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