# SIMPLE DERIVATION OF A STATE OBSERVER OF LINEAR TIME-VARYING DISCRETE SYSTEMS

### Yasuhiko Mutoh

#### Abstract

In this paper, a simple calculation method to derive the Luenberger observer for linear time-varying discrete systems is presented. For this purpose, the simple design method of the pole placement for linear time-varying discrete systems is proposed. 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 new 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 discrete system, the state observer can be derived by simple calculations.

#### References

- Kwakaernaak H. C., Linear Optimal Control Systems. Wiley-Interscience, 1972
- Chi-Tsong Chen C., Linear System Theory and Design (Third edition). Oxford University Press, 1999
- T. Kailath C., Linear Systems. Prentice-Hall, 1980
- Tse E., and Athans M., Optimal Minimal-Order ObserverEstimators for Discrete Linear Time-Varying System. IEEE, Transaction on AC, AC-15, 4, 416-426, 1970
- Mutoh Y, Simple Design of the State Observer for Linear Time-Varying Systems. 6-th ICINCO, 2009

#### Paper Citation

#### in Harvard Style

Mutoh Y. (2010). **SIMPLE DERIVATION OF A STATE OBSERVER OF LINEAR TIME-VARYING DISCRETE SYSTEMS** . In *Proceedings of the 7th International Conference on Informatics in Control, Automation and Robotics - Volume 3: ICINCO,* ISBN 978-989-8425-02-7, pages 30-34. DOI: 10.5220/0002945800300034

#### in Bibtex Style

@conference{icinco10,

author={Yasuhiko Mutoh},

title={SIMPLE DERIVATION OF A STATE OBSERVER OF LINEAR TIME-VARYING DISCRETE SYSTEMS},

booktitle={Proceedings of the 7th International Conference on Informatics in Control, Automation and Robotics - Volume 3: ICINCO,},

year={2010},

pages={30-34},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0002945800300034},

isbn={978-989-8425-02-7},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 7th International Conference on Informatics in Control, Automation and Robotics - Volume 3: ICINCO,

TI - SIMPLE DERIVATION OF A STATE OBSERVER OF LINEAR TIME-VARYING DISCRETE SYSTEMS

SN - 978-989-8425-02-7

AU - Mutoh Y.

PY - 2010

SP - 30

EP - 34

DO - 10.5220/0002945800300034