Email this article 
THE GREATEST SOLUTION IN THE INEQUALITY OF K X X LX WITH K 2 ISnn;L 2 ISnn;X 2 ISnm ARE A COMPLETE IDEMPOTENT SEMIRINGS OF INTERVAL
https://doi.org/10.22146/jmt.56567 Eka Susilowati(1*)
(1) Universitas PGRI Adi Buana Surabaya
(*) Corresponding Author
Abstract
The greatest solution of an inequality K
X X LX to solve the optimal
control problem for P-Temporal Event Graphs, which is to nd the optimal control that
meets the constraints on the output and constraints imposed on the adjusted model prob-
lem (the model matching problem). We give the greatest solution K
X X L X
and X H with K; L;X;H matrices whose are entries in a complete idempotent semir-
ings. Furthermore, the authors examine the existence of a sucient condition of the
projector in the set of solutions of inequality K
X X L X with K; L;X matrix
whose entries are in the complete idempotent semiring. Projectors can be very necessary
to synthesize controllers in manufacturing systems that are constrained by constraints
and some industrial applications. The researcher then examines the requirements for
the presence of the greatest solution was called projector in the set of solutions of the
inequality K
X X L X with K; L;X matrices whose are entries in an complete
idempotent semiring of interval. Researchers describe in more detail the proof of the
properties used to resolve the inequality K
X X L X. Before that, we give
the greatest solution of the inequality K
X X LX and X G with K; L;X;G
matrices whose are entries in an complete idempotent semiring of interval
Keywords
Full Text:
PDF Eka SusilowatiReferences
Andersen, M.H.,Max - plus Algebra : Properties and Applications, Laramie, WY, 2002
Baccelli, F., Cohen, G., Olsder, J., dan Quadrat, J.P., Synchronization and Linearity, An Algebra
for Discrete Event Systems, John Wiley and Sons, New York, 1992
Brunsch, T., Hardouin, L., dan Raisch, J.,Modeling Control of Nested Manufacturing Processes
Using Dioid Models, In Peprints of the 3rd International Workshop on Dependable Control of
Discrete Systems, Germany, 2011
Brunsch, T., Hardouin, L., Maia, C. A., dan Raisch, J., Duality and Interval Analysis Over
Idempotent Semirings, Linear Algebra and Its Applications 437, 2436 - 2454,2012
Brunsch, T., Hardouin, L., Boutin, O., Cottenceau, B., dan Raisch, J., Discrete Event Systems in
a Dioid Framework: Control Theory, Control of Discrete Event Systems, Volume 433 of Lecture
Notes in Control and Information Sciences, Springer, Berlin, 2013
Brunsch, T., Dissertation : Modeling and Control of Complex Systems in A Dioid Frame Work,
Berlin, 2014
Cohen, G., Gaubert, S., dan Quadrat, J.P., Max plus Algebra and System Theory : Where We
Are and Where to Go Now, IFAC Conference on Systems and Control, 1998
Gaubert, S., Methods and Application of (max, +) Linear Algebra, Rapport de Recherche, 1997
Hardouin, L., Cottenceau, B., Le Corronc, E., Control of uncertain (max,+)-linear system in
order to decrease uncertainty, University of Angers, 2010
Hardouin, L., Cottenceau, B., Le Corronc, E., On The Dual Product and The Dual Residuation
over Idempotent Semiring of Intervals, University of Angers, Perancis,2010
Houssin, L., Lahaye, S., dan Boimond, J.L., Control of (Max,+) - Linear Systems Minimizing
Delays, University of Angers, Perancis, 2008
Judson, T.W., Abstract Algebra : Theory and Applications, Stephen F. Austin State University,
Lhommeau, M., Hardouin, L., Cottenceau, B., Disturbance Decoupling of Timed Event Graphs by
Output Feedback Controller, University of Angers, 2009
Lhommeau, M., Hardouin, L., Cottenceau, B., Maia, C.A., Observer Design for (max,plus) Linear
Systems, IEEE Transaction on Automatic Control vol. 55-2, 2010
DOI: https://doi.org/10.22146/jmt.56567
Article Metrics
Abstract views : 1683
| 
views : 1302
Refbacks
- There are currently no refbacks.
Copyright of Jurnal Matematika Thales ISSN 2715-1891 (Print).
Jumlah Kunjungan: View My Stats
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.