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Discretising effectively a linear singular differential system by choosing an appropriate sampling period

Discretising effectively a linear singular differential system by choosing an appropriate sampling period

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Two main goals are to discretise the solution of an autonomous linear singular continuous-time system and to compare the discretised with the continuous solution at fixed time moments. Practically speaking, we are interested in such kind of systems, since they are inherent in many physical, economical and engineering phenomena. The complex Kronecker canonical form decomposes the singular system into five sub-systems, whose solutions are obtained. Moreover, in order for the norm of the difference between the two solutions to be smaller than a fully pre-defined, acceptable bound, the sampling period should be arranged in a particular interval. A numerical example is also available.

References

    1. 1)
      • K.E. Brenan , S.L. Campbell , L.R. Petzold . (1996) Numerical solution of initial-value problems in differential–algebraic equations.
    2. 2)
      • S.L. Campbell . (1980) Singular systems of differential equations.
    3. 3)
      • L. Dai . (1989) Singular control systems.
    4. 4)
      • D.G. Luenberger , A. Arbel . (1977) Singular dynamic Leontief systems.
    5. 5)
      • V. Mehrmann . (1991) The autonomous linear quadratic control problem: theory and numerical solution.
    6. 6)
      • W. Leontief . (1986) Input–output economics.
    7. 7)
      • D.A. Kendrick . On the Leontief dynamic inverse. Quart. J. Econ. , 693 - 696
    8. 8)
    9. 9)
      • R.G. Kreijger , H. Neudecker . Kendrick's forward integration method and the dynamic Leontief multisectoral model. Quart. J. Econ. , 505 - 507
    10. 10)
      • Kalogeropoulos, G.I., Pantelous, A.A.: `Can be linear difference descriptor systems appeared in Insurance?', Proc. 7th Int. Conf. Applied Mathematics, 2008, Bratislava Slovakia, p. 467–478.
    11. 11)
      • Kalogeropoulos, G.I., Karageorgos, A.D., Pantelous, A.A.: `Comparing the solutions of autonomous generalized linear continuous and discrete-time systems', Proc. 8th Portuguese Conf. Automatic Control, CONTROLO2008, 2008, Utad-Vila Real, Portugal.
    12. 12)
      • Verghese, G.: `Infinite frequency behaviour in generalized dynamical systems', 1978, PhD, Stanford University, USA.
    13. 13)
      • N. Karancias . Matrix pencil approach to geometric system theory. Proc. IEE , 585 - 590
    14. 14)
      • Karcanias, N., Hayton, G.E.: `Generalised autonomous differential systems, algebraic duality, and geometric theory', Proc. IFAC VIII, Triennial World Congress, 1981, Kyoto, Japan.
    15. 15)
      • P. Van Dooren . (1983) Reducing subspaces: definitions, properties, and algorithms, in matrix pencils.
    16. 16)
      • Kalogeropoulos, G.I.: `Matrix pencils and linear systems', 1980, PhD, City University, London.
    17. 17)
      • E. Grispos . Singular generalized autonomous linear differential systems. Bull. Greek Math. Soc. , 25 - 43
    18. 18)
      • D.G. Forney . Minimal bases of rational vector spaces with application to multivariable systems. SIAM J. Control , 493 - 520
    19. 19)
      • F.L. Lewis . A survey of linear singular systems. Circuits Syst. Signal Process. , 1 , 3 - 36
    20. 20)
      • F.R. Gantmacher . (2000) The theory of matrices.
    21. 21)
      • P.N. Karampetakis . On the discretization of singular systems. IMA J. Math. Control Inf. , 223 - 242
    22. 22)
      • F.N. Koumboulis , B.G. Mertzios . On Kalman's controllability and observability criteria for singular systems. Circuit Syst. Signal Process. , 269 - 290
    23. 23)
      • A. Rachid . A remark on the discretization of singular systems. Automatica , 347 - 348
    24. 24)
      • Kytagias, D.: `An algorithmic method of computation of the reduced set of quadratic Plücker relations and applications in feedback problems of regular and singular control systems', 1993, PhD, University of Athens, Greece.
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