# SIMPLE DESIGN OF THE STATE OBSERVER FOR LINEAR TIME-VARYING SYSTEMS

### Yasuhiko Mutoh

#### Abstract

A simple design method of the Luenberger observer for linear time-varying systems is proposed in this paper. The paper first propose the simple calculation method to derive the pole placement feedback gain vector for linear time-varying systems. For this purpose, it is shown that the pole placement controller can be derived simply by finding some particular ”output signal” such that the relative degree from the input to this output is equal to the order of the system. Using this fact, the feedback gain vector can be calculated directly from plant parameters without transforming the system into any standard form. Then, this method is applied to the design of the observer, i.e., because of the duality of linear time-varying system, the state observer can be derived by un-stabilization of the state error equation.

#### References

- Charles C. NguyenC Arbitrary eigenvalue assignments for linear time-varying multivariable control systems. International Journal of Control, 45-3, 1051-1057, 1987
- Chi-Tsong ChenC Linear System Theory and Design (Third edition). OXFORD UNIVERSITY PRESS, 1999
- T. KailathC Linear Systems. Prentice-Hall, 1980
- Michael Valás?ek, Nejat Olgac¸ Efficient Eigenvalue Assignment for General Linear MIMO systems. Automatica, 31-11, 1605-1617, 1995
- Michael Valás?ek, Nejat Olgac¸C Pole placement for linear time-varying non-lexicographically fixed MIMO systems. Automatica, 35-1, 101-108, 1999

#### Paper Citation

#### in Harvard Style

Mutoh Y. (2009). **SIMPLE DESIGN OF THE STATE OBSERVER FOR LINEAR TIME-VARYING SYSTEMS** . In *Proceedings of the 6th International Conference on Informatics in Control, Automation and Robotics - Volume 2: ICINCO,* ISBN 978-989-674-001-6, pages 225-229. DOI: 10.5220/0002206002250229

#### in Bibtex Style

@conference{icinco09,

author={Yasuhiko Mutoh},

title={SIMPLE DESIGN OF THE STATE OBSERVER FOR LINEAR TIME-VARYING SYSTEMS},

booktitle={Proceedings of the 6th International Conference on Informatics in Control, Automation and Robotics - Volume 2: ICINCO,},

year={2009},

pages={225-229},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0002206002250229},

isbn={978-989-674-001-6},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 6th International Conference on Informatics in Control, Automation and Robotics - Volume 2: ICINCO,

TI - SIMPLE DESIGN OF THE STATE OBSERVER FOR LINEAR TIME-VARYING SYSTEMS

SN - 978-989-674-001-6

AU - Mutoh Y.

PY - 2009

SP - 225

EP - 229

DO - 10.5220/0002206002250229