Pointwise completeness and pointwise degeneracy of positive fractional descriptor continuous-time linear systems with regular pencils are addressed. Conditions for pointwise completeness and pointwise degeneracy of the systems are established and illustrated by an example.
@article{bwmeta1.element.bwnjournal-article-amcv25i2p217bwm,
author = {Tadeusz Kaczorek},
title = {Pointwise completeness and pointwise degeneracy of positive fractional descriptor continuous-time linear systems with regular pencils},
journal = {International Journal of Applied Mathematics and Computer Science},
volume = {25},
year = {2015},
pages = {217-221},
zbl = {1321.93042},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-amcv25i2p217bwm}
}
Tadeusz Kaczorek. Pointwise completeness and pointwise degeneracy of positive fractional descriptor continuous-time linear systems with regular pencils. International Journal of Applied Mathematics and Computer Science, Tome 25 (2015) pp. 217-221. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-amcv25i2p217bwm/
[000] Bru, R., Coll, C., Romero-Vivo, S. and Sanchez, E. (2003). Some problems about structural properties of positive descriptor systems, in L. Benvenuti, A. de Santis and L. Farina (Eds.), Positive Systems, Lecture Notes in Control and Information Sciences, Vol. 294, Springer, Berlin, pp. 233-240. | Zbl 1060.93065
[001] Bru, R., Coll, C. and Sanchez, E. (2002). Structural properties of positive linear time-invariant difference-algebraic equations, Linear Algebra and Its Applications 349(1-3): 1-10. | Zbl 1006.93006
[002] Busłowicz, M. (2008). Pointwise completeness and pointwise degeneracy of linear discrete-time systems of fractional order, Zeszyty Naukowe Politechniki Śląskiej: Automatyka (151): 19-24, (in Polish).
[003] Busłowicz, M., Kociszewski, R., Trzasko, W. (2006). Pointwise completeness and pointwise degeneracy of positive discrete-time systems with delays, Zeszyty Naukowe Politechniki Śląskiej: Automatyka (145): 55-56, (in Polish).
[004] Choundhury, A.K. (1972). Necessary and sufficient conditions of pointwise completeness of linear time-invariant delay-differential systems, International Journal of Control 16(6): 1083-1100. | Zbl 0245.93019
[005] Campbell, S.L., Meyer, C.D. and Rose, N.J. (1976). Applications of the Drazin inverse to linear systems of differential equations with singular constant coefficients, SIAM Journal Applied Mathematics 31(3): 411-425. | Zbl 0341.34001
[006] Dai, L. (1989). Singular Control Systems, Lectures Notes in Control and Information Sciences, Vol. 118, Springer-Verlag, Berlin. | Zbl 0669.93034
[007] Guang-Ren, D. (2010). Analysis and Design of Descriptor Linear Systems, Springer, New York, NY. | Zbl 1227.93001
[008] Farina, L. and Rinaldi, S. (2000). Positive Linear Systems: Theory and Applications, J. Wiley, New York, NY. | Zbl 0988.93002
[009] Kaczorek, T. and Busłowicz, M. (2009). Pointwise completeness and pointwise degeneracy of linear continuous-time fractional order systems, Journal of Automation, Mobile Robotics & Intelligent Systems 3(1): 8-11.
[010] Kaczorek, T. (1992). Linear Control Systems, Vol. 1, Research Studies Press J. Wiley, New York, NY. | Zbl 0784.93002
[011] Kaczorek, T. (2002). Positive 1D and 2D Systems, Springer-Verlag, London. | Zbl 1005.68175
[012] Kaczorek, T. (2004). Infinite eigenvalue assignment by an output feedback for singular systems, International Journal of Applied Mathematics and Computer Science 14(1): 19-23. | Zbl 1171.93331
[013] Kaczorek, T. (2009). Pointwise completeness and pointwise degeneracy of standard and positive fractional linear systems with state-feedbacks, Archives of Control Sciences 19(3): 295-306. | Zbl 1298.93179
[014] Kaczorek, T. (2010). Pointwise completeness and pointwise degeneracy of standard and positive linear systems with state-feedbacks, JAMRIS 4(1): 3-7. | Zbl 1298.93179
[015] Kaczorek, T. (2011a). Checking of the positivity of descriptor linear systems by the use of the shuffle algorithm, Archives of Control Sciences 21(3): 287-298. | Zbl 1264.93096
[016] Kaczorek, T. (2011b). Pointwise completeness and pointwise degeneracy of 2D standard and positive Fornasini-Marchesini models, COMPEL 30(2): 656-670. | Zbl 1225.93062
[017] Kaczorek, T. (2011c). Reduction and decomposition of singular fractional discrete-time linear systems, Acta Mechanica et Automatica 5(4): 62-66.
[018] Kaczorek, T. (2011d). Selected Problems of Fractional Systems Theory, Springer-Verlag, Berlin. | Zbl 1221.93002
[019] Kaczorek, T. (2011e). Singular fractional discrete-time linear systems, Control and Cybernetics 40(3): 753-761. | Zbl 1318.93058
[020] Kaczorek, T. (2013). Application of Drazin inverse to analysis of descriptor fractional discrete-time linear systems with regular pencils, International Journal of Applied Mathematics and Computer Science 23(1): 29-33, DOI: 10.2478/amcs-2013-0003. | Zbl 1293.93496
[021] Kaczorek, T. (2014a). Drazin inverse matrix method for fractional descriptor continuous-time linear systems, Bulletin of the Polish Academy of Sciences: Technical Sciences 62(2): 409-412.
[022] Kaczorek, T. (2014b). Minimum energy control of positive fractional descriptor continuous-time linear systems, IET Control Theory and Applications 8(1): 219-225.
[023] Olbrot, A. (1972). On degeneracy and related problems for linear constant time-lag systems, Ricerche di Automatica 3(3): 203-220.
[024] Popov, V.M. (1972). Pointwise degeneracy of linear time-invariant delay-differential equations, Journal of Differential Equations 11: 541-561. | Zbl 0238.34107
[025] Trzasko, W., Busłowicz, M. and Kaczorek, T. (2007). Pointwise completeness of discrete-time cone-systems with delays, EUROCON, Warsaw, Poland, pp. 606-611.
[026] Weiss, L. (1970). Controllability for various linear and nonlinear systems models, in J.A. Yorke, Seminar on Differential Equations and Dynamical Systems II, Lecture Notes in Mathematics, Vol. 144, Springer, Berlin, pp. 250-262.
[027] Virnik (2008). Stability analysis of positive descriptor systems, Linear Algebra and Its Applications 429(10): 2640-2659. | Zbl 1147.93033