# Direct algorithm for pole placement by state-derivative feedback for multi-inputlinear systems - nonsingular case

Kybernetika (2005)

• Volume: 41, Issue: 5, page [637]-660
• ISSN: 0023-5954

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## Abstract

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This paper deals with the direct solution of the pole placement problem by state-derivative feedback for multi- input linear systems. The paper describes the solution of this pole placement problem for any controllable system with nonsingular system matrix and nonzero desired poles. Then closed-loop poles can be placed in order to achieve the desired system performance. The solving procedure results into a formula similar to Ackermann one. Its derivation is based on the transformation of linear multi-input systems into Frobenius canonical form by coordinate transformation, then solving the pole placement problem by state derivative feedback and transforming the solution into original coordinates. The procedure is demonstrated on examples. In the present work, both time- invariant and time-varying systems are treated.

## How to cite

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Abdelaziz, Taha H. S., and Valášek, Michael. "Direct algorithm for pole placement by state-derivative feedback for multi-inputlinear systems - nonsingular case." Kybernetika 41.5 (2005): [637]-660. <http://eudml.org/doc/33779>.

@article{Abdelaziz2005,
abstract = {This paper deals with the direct solution of the pole placement problem by state-derivative feedback for multi- input linear systems. The paper describes the solution of this pole placement problem for any controllable system with nonsingular system matrix and nonzero desired poles. Then closed-loop poles can be placed in order to achieve the desired system performance. The solving procedure results into a formula similar to Ackermann one. Its derivation is based on the transformation of linear multi-input systems into Frobenius canonical form by coordinate transformation, then solving the pole placement problem by state derivative feedback and transforming the solution into original coordinates. The procedure is demonstrated on examples. In the present work, both time- invariant and time-varying systems are treated.},
author = {Abdelaziz, Taha H. S., Valášek, Michael},
journal = {Kybernetika},
keywords = {pole placement; state-derivative feedback; linear MIMO systems; feedback stabilization; pole placement; state-derivative feedback; linear MIMO system; feedback stabilization},
language = {eng},
number = {5},
pages = {[637]-660},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Direct algorithm for pole placement by state-derivative feedback for multi-inputlinear systems - nonsingular case},
url = {http://eudml.org/doc/33779},
volume = {41},
year = {2005},
}

TY - JOUR
AU - Abdelaziz, Taha H. S.
AU - Valášek, Michael
TI - Direct algorithm for pole placement by state-derivative feedback for multi-inputlinear systems - nonsingular case
JO - Kybernetika
PY - 2005
PB - Institute of Information Theory and Automation AS CR
VL - 41
IS - 5
SP - [637]
EP - 660
AB - This paper deals with the direct solution of the pole placement problem by state-derivative feedback for multi- input linear systems. The paper describes the solution of this pole placement problem for any controllable system with nonsingular system matrix and nonzero desired poles. Then closed-loop poles can be placed in order to achieve the desired system performance. The solving procedure results into a formula similar to Ackermann one. Its derivation is based on the transformation of linear multi-input systems into Frobenius canonical form by coordinate transformation, then solving the pole placement problem by state derivative feedback and transforming the solution into original coordinates. The procedure is demonstrated on examples. In the present work, both time- invariant and time-varying systems are treated.
LA - eng
KW - pole placement; state-derivative feedback; linear MIMO systems; feedback stabilization; pole placement; state-derivative feedback; linear MIMO system; feedback stabilization
UR - http://eudml.org/doc/33779
ER -

## References

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