Discretization of singular systems and error estimation

• Autorzy: Nicholas P. Karampetakis , Rallis Karamichalis
• Języki publikacji: EN

Abstrakty

EN

This paper proposes a discretization technique for a descriptor differential system. The methodology used is both triangular first order hold discretization and zero order hold for the input function. Upper bounds for the error between the continuous and the discrete time solution are produced for both discretization methods and are shown to be better than any other existing method in the literature.

Słowa kluczowe

EN

descriptor systems; discretization; truncation error; first order hold; zero order hold

• Wydawca: University of Zielona Gora Press
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2014
• Tom: 24
• Numer: 1
• Strony: 65-73

Daty

wydano

2014

otrzymano

2013-01-18

poprawiono

2013-07-26

Twórcy

autor

Nicholas P. Karampetakis

• Department of Mathematics, Aristotle University of Thessaloniki, Thessaloniki 54124, Greece

autor

Rallis Karamichalis

• Department of Mathematics, Aristotle University of Thessaloniki, Thessaloniki 54124, Greece

Bibliografia

• Basterretxea, K., Bárcena, R. and Ugalde, U. (2008). Design and synthesis of a configurable fractional order hold device for sampled-data control systems, WSEAS Transactions on Circuits and Systems 7(8): 869-878.
• Chen, C.-M. and Wang, K.-H. (1999). State-space model conversion of a system with state delay, Proceedings of the National Science Council, Republic of China, Part A: Physical Science and Engineering 23(6): 782-788.
• Dai, L. (1989). Singular Control Systems, Lecture Notes in Control and Information Sciences, Vol. 118, Springer-Verlag, Berlin.
• Davidson, K.R. and Donsig, A.P. (2010). Real Analysis and Applications: Theory in Practice, Undergraduate Texts in Mathematics, Springer, New York, NY.
• Duan, G. (2010). Analysis and Design of Descriptor Linear Systems, Advances in Mechanics and Mathematics, Vol. 23, Springer New York, NY.
• Franklin, G.F., Workman, M.L. and Powell, D. (1997). Digital Control of Dynamic Systems, Addison-Wesley Longman Publishing Co., Inc., Boston, MA.
• Gantmacher, F. (1959). The Theory of Matrices, Vol. I, Chelsea, New York, NY..
• Jugo, J. (2002). Discretization of continuous time-delay systems, 15th IFAC World Congress on Automatic Control, Barcelona, Spain, p. 586.
• Jury, E.I. (1958). Sampled Data Control Systems, Wiley, New York, NY.
• Kaczorek, T. (2003). Canonical forms of singular 1D and 2D linear systems, International Journal of Applied Mathematics and Computer Science 13(1): 61-72.
• Kaczorek, T. (2013). Descriptor fractional linear systems with regular pencils, International Journal of Applied Mathematics and Computer Science 23(2): 309-315, DOI: 10.2478/amcs-2013-0023.
• Karageorgos, A., Pantelous, A. and Kalogeropoulos, G. (2010). Discretizing LTI descriptor (regular) differential input systems with consistent initial conditions, Advances in Decision Sciences 2010, Article ID: 810605.
• Karageorgos, A., Pantelous, A. and Kalogeropoulos, G. (2011). Designing the sampling period of a discretized LTI descriptor (regular) system with inputs, International Journal of Control, Automation and Systems 9(4): 791-796.
• Karampetakis, N. and Gregoriadou, A. (2011). On a first order hold discretization for singular systems, International Conference on Communications, Computing and Control Applications (CCCA'11), Hammamet, Tunisia, http://dx.doi.org/10.1109/CCCA.2011.6031414.
• Karampetakis, N. P. (2004). On the discretization of singular systems, IMA Journal of Mathematical Control and Information 21(2): 223-242.
• Koumboulis, F.N. and Mertzios, B.G. (1999). On Kalman's controllability and observability criteria for singular systems, Circuits Systems and Signal Processing 18(3): 269-290.
• Levine, W. (2008). The Control Handbook, CRC Press, Boca Raton, FL.
• López-Estrada, F.-R., Theilliol, D., Astorga Zaragoza, C.M. and Ponsart, J.-C. (2012). Developments of a Scilab/Matlab toolbox dedicated to LTI/LPV descriptor systems for fault diagnosis, 10th European Workshop on Advanced Control and Diagnosis, ACD 2012, Copenhagen, Denmark, (on CD-ROM).
• Sincovec, R., Erisman, A., Yip, E. and Epton, M. (1981). Analysis of descriptor systems using numerical algorithms, IEEE Transactions on Automatic Control 26(1): 139-147.
• Toshiyuki, H.T.Y. and Mituhiko, A. (1993). Stability of the limiting zeros of sampled-data systems with zero-and first-order holds, International Journal of Control 58(6): 1325-1346.
• Vardulakis, A.I.G. (1991). Linear Multivariable Control: Algebraic Analysis and Synthesis Methods, Wiley, Hoboken, NJ.
• Vardulakis, A. and Karcanias, N. (1983). Relations between strict equivalence invariants and structure at infinity of matrix pencils, IEEE Transactions on Automatic Control 28(4): 514-516.

Identyfikatory

DOI

10.2478/amcs-2014-0005