# Block Triangular Decoupling of General Neutral Multi Delay Systems

### Fotis N. Koumboulis, Nikolaos D. Kouvakas

#### Abstract

The problem of block triangular decoupling is studied for the case of general neutral multi delay systems. The system is not restricted to be square and invertible. The controller is of the general neutral dynamic type involving a dynamic feedback and dynamic precompensator. Two different cases of feedback are studied. The first is the case of measurable output feedback and second is the case of performance output feedback. The controller is restricted to be realizable. The necessary and sufficient conditions for the problem to be solvable are established. The general class of the realizable controllers solving the problem is derived. The closed loop transfer function is proven to have arbitrary characteristic polynomial thus facilitating command tracking and stability.

#### References

- Caturiyati, dan S.W., 2003. The Application of Block Triangular Decoupling for Linear Systems over Principal Ideal Domains on the Pole Assignment, In Proceedings of the SEAMS-GMU (Southeast Asian Mathematical Society-Gadjah Mada University) International Conference on Mathematics and its Applications, UGM, pp. 83-92, July 14-17.
- Commault, C., Dion, J. M., 1983. Transfer Matrix Approach to the Triangular Block Decoupling Problem, In Automatica, vol. 19, pp. 533-542.
- Ito, N., Inaba, H. 1997. Block triangular decoupling and pole assignment for linear systems over principal ideal domains, In Proceedings of the 36th IEEE Conference on Decision and Control, 10-12 Dec, vol.1, pp. 318-323.
- Ito, N., Inaba, H., 1997. Block Triangular Decoupling for Linear Systems over Principal Ideal Domains, In SIAM Journal on Control and Optimization, vol. 35, no. 3, pp. 744-765.
- Koumboulis, F. N., Kouvakas, N. D., 2010. Triangular Decoupling of nonsquare general neutral time delay systems via dynamic measurement output feedback with application to an ASP, In Proceedings of the 15th International Conference on Emerging Technologies and Factory Automation, pp. 1-10, September 13-16, Bilbao, Spain.
- Koumboulis, F. N., Kouvakas, N. D., 2011. Block Decoupling of General Neutral Multi Delay Systems, 16th IEEE International Conference on Emerging Technologies and Factory Automation, pp. 1-6, September 5-9, Toulouse, France.
- Koumboulis, F. N., Kouvakas, N. D., Paraskevopoulos, P.N., 2009. Linear approximant-based metaheuristic proportional-integral-derivative controller for a neutral time delay central heating system, In Proceedings of the IMechE Part I: Journal of Systems and Control Engineering, vol. 223, pp. 605-618.
- Koumboulis, F. N., Kouvakas, N. D., Paraskevopoulos, P.N., 2009. On the Morgan's Problem for Neutral Time Delay Systems via Dynamic Controllers with application to a Test Case Central Heating System, In Proceedings of the 3rd IEEE Multi-conference on Systems and Control (MSC 2009), pp. 1195-1992, Saint Petersburg, Russia, July 8-10.
- Koumboulis, F. N., Kouvakas, N. D., Paraskevopoulos, P.N., 2009., Velocity Control and Vibration Attenuation for a Cart-Pendulum System with Delayed Resonators, In Proceedings of the 3rd IEEE Multiconference on Systems and Control (MSC 2009), pp. 1180-1187, Saint Petersburg, Russia, July 8-10.
- Koumboulis, F. N., Panagiotakis, G. E., 2008. Transfer matrix approach to the triangular decoupling of general neutral multi-delay systems, In Proceedings of the 17th IFAC World Congress, pp. 1279-1286, July 6- 11, Seoul, Korea.
- Lohmann, B., 1991. Partial decoupling of non-minimum phase systems by constant state feedback, In Kybernetika, vol. 27, no. 5, pp. 436-445.
- Morse, A., Wonham, W. M., 1970. Triangular decoupling of linear multivariable systems, In IEEE Transactions on Automatic Control, vol. 15, pp. 447-449.
- Otsuka N., Inaba, H., 1992. The Simultaneous Block Triangular Decoupling, Disturbance Rejection and Pole Assignment Problem for Linear Multivariable Systems, In Transactions of the Society of Instrument and Control Engineers, vol.28, no.7, pp. 796-800.
- Otsuka, N., 1992. Simultaneous Block TriangularDecoupling and Disturbance-Rejection Problem with Incomplete-State Feedback, In Transactions of the Society of Instrument and Control Engineers, vol.28, no.3, pp. 320-32.
- Park, K., 2008. Existence Conditions of Decoupling Controllers in the Generalized Plant Model, In Proceedings of the 47th IEEE Conference on Decision and Control, Cancun, Mexico, Dec. 9-11, pp. 5158-5163.
- Park, K., Choi, G-H., 2011. Necessary and Sufficient Conditions for the Existence of Decoupling Controllers in the Generalized Plant Model, In Journal of Electrical Engineering & Technology, vol. 6, No. 5, pp. 706-712.
- Sourlas, D. D., 2001. Optimization-based decoupling controller design for discrete systems, In Chemical Engineering Science, vol. 56, pp. 4695-4710.

#### Paper Citation

#### in Harvard Style

N. Koumboulis F. and D. Kouvakas N. (2012). **Block Triangular Decoupling of General Neutral Multi Delay Systems** . In *Proceedings of the 9th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,* ISBN 978-989-8565-21-1, pages 542-547. DOI: 10.5220/0004048205420547

#### in Bibtex Style

@conference{icinco12,

author={Fotis N. Koumboulis and Nikolaos D. Kouvakas},

title={Block Triangular Decoupling of General Neutral Multi Delay Systems},

booktitle={Proceedings of the 9th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,},

year={2012},

pages={542-547},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0004048205420547},

isbn={978-989-8565-21-1},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 9th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,

TI - Block Triangular Decoupling of General Neutral Multi Delay Systems

SN - 978-989-8565-21-1

AU - N. Koumboulis F.

AU - D. Kouvakas N.

PY - 2012

SP - 542

EP - 547

DO - 10.5220/0004048205420547