Optimum Complementary Control for Stable Systems of the Positive Linear Time Invariant

Authors

  • Nurweni Putri Universitas Dharma Andalas
  • Iswan Rina

DOI:

https://doi.org/10.20956/j.v17i3.13379

Keywords:

Positive Stable MIMO System, Optimal Complementary Control, Hurwitz Matrix, Constant Disturbace

Abstract

The optimal control problem is defined as a problem in selecting a controller u(t) in a continuous linear system, so that it can provide the optimum value for a given objective function. The u(t) controller is expected to control the system so that it produces the desired output. In this research, it will be studied about how to select and construct the optimal controller u(t) in the Linear Time Invariant MIMO system positive stable, so that the given system will remain positive when given constant disturbance

References

Ariyanti Gregoria. 2020. Necessary and Sufficient Conditions for The Solutions of Linear Equations System. Jurnal Matematika, stattistika dan Komputasi, Vol.17 No.1, 82-88.

Arif D., Adzkiya D., Apriliani E., & Khasanah I. 2017. Model Reduction of Non-minimal Discrete-Time Linear-Time-Invariant Systems. MJMS

Beauthier, C. dan Joseph J. Winkin. 2010. LQ-Optimal Control of Positive Linear System. Wiley Online Library.

Farina, L. dan Rinaldi, S. 2000. Positive Linear Systems : Theory and Aplications. Wiley. New York.

Firman. 2011. Modifikasi Kontro untuk Sistem Tak Linier Input Tunggal-Output Tunggal. Jurnal Matematika, stattistika dan Komputasi, Vol.7 No.2, 118-123.

Guo Zongyi, David H., Jianguo G., Zheng W., Jarome & Jing C. 2020. Metzler Matrix-Based Switching Control Scheme For Linear Systems With Prescribed Performance Guarantees. IFAC-PapersOnLine 53-2 (2020) 6428-6433.

Hendricks. Elbert, Ole. Jannerup dan P. H. Sorensen. 2008. Linear Systems Control. Springer- Verlag Berlin Heidelberg.

Kaczorek, T. 2001. Positive 1D and 2D Systems Metzler Matrices. SpringerVerlag Berlin Heidelberg.

Krokavec D. & Filasova A. 2020. Reduced-Order Observers for Linear Metzlerian Systems. IFAC-PapersOnLine 53-2 (2020) 4553-6558.

Kundu A., Daafouz J., & Heemels. 2017. Stabilization of Discrete-Time Switched Linear Systems: Lyapunov-Metzler Inequalities versus S-procedure characterizations. IFAC-PapersOnLine 50-1 (2017) 3412-3417.

Leenheer, P. dan D. Aeyels. 2001. Stabilization of Positive Linear Systems. Systems and Control Letters. 44: 259-271.

Meyer. Carl D. 2000. Matrix Analysis and Applied Linear Algebra. SIAM

Mitkowski. W. 2008. Dynamical Properties of Metzler Systems. Bulletin of The Polish Academy of Sciences Technical Sciences. Vol. 56, No. 4.

Naidu, D.S. 2002. Optimal Control Systems. CRC Press, Idaho.

Rama K. Yedavalli. 2018. Conditions for Hurwitz Stability / Instability of a Real matrix via its Sign Pattern with a Necessary and Sufficent Condition for Magnitude Independent Stability. IFAC-PapersOnLine 51-1 (2018) 663-667.

Richard, Charles Jhonson. 1982. Inverse M-Matrices. Algebra Linear and Its Applications 47:195-216.

Roszak, B. dan Davidson, E. J. 2009. Necessary and Sufficient Conditions for Stabilizability of Positive LTI System. System and Control Letters 58(2009). 474-481.

Roszak, B. dan Davidson, E. J. 2010. The Multivariable Servomechanism controller for SISO positive LTI System. IEEE Transactions on Automatic Control, 55(9), 2204-2209.

Downloads

Published

2021-05-12

Issue

Section

Research Articles