Pointwise completeness and pointwise degeneracy of positive fractional descriptor continuous-time linear systems with regular pencils

Tadeusz Kaczorek

doi:10.1515/amcs-2015-0016

$Pointwise completeness and pointwise degeneracy of positive fractional descriptor continuous-time linear systems with regular pencils Cover$

.blurhash-client-img { display: none !important; }

Pointwise completeness and pointwise degeneracy of positive fractional descriptor continuous-time linear systems with regular pencils

International Journal of Applied Mathematics and Computer Science

Volume 25 (2015): Issue 2 (June 2015)

By: Tadeusz Kaczorek

Open Access

|Jun 2015

Abstract

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.

References

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. 233-240.10.1007/978-3-540-44928-7_32
Search in Google Scholar
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): 1-10.10.1016/S0024-3795(02)00277-X
Search in Google Scholar
Busłowicz, M. (2008). Pointwise completeness and pointwise degeneracy of linear discrete-time systems of fractional order, Zeszyty Naukowe Politechniki S´la˛skiej: Automatyka (151): 19-24, (in Polish).
Search in Google Scholar
Busłowicz, M., Kociszewski, R., Trzasko, W. (2006). Pointwise completeness and pointwise degeneracy of positive discrete-time systems with delays, Zeszyty Naukowe Politechniki Slaskiej: Automatyka (145): 55-56, (in Polish).
Search in Google Scholar
Choundhury, A.K. (1972). Necessary and sufficient conditions of pointwise completeness of linear time-invariant delay-differential systems, International Journal of Control 16(6): 1083-1100.10.1080/00207177208932341
Search in Google Scholar
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): 411-425.10.1137/0131035
Search in Google Scholar
Dai, L. (1989). Singular Control Systems, Lectures Notes in Control and Information Sciences, Vol. 118, Springer-Verlag, Berlin.
Search in Google Scholar
Guang-Ren, D. (2010). Analysis and Design of Descriptor Linear Systems, Springer, New York, NY.10.1007/978-1-4419-6397-0_3
Search in Google Scholar
Farina, L. and Rinaldi, S. (2000). Positive Linear Systems: Theory and Applications, J. Wiley, New York, NY.10.1002/9781118033029
Search in Google Scholar
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.
Search in Google Scholar
Kaczorek, T. (1992). Linear Control Systems, Vol. 1, Research Studies Press J. Wiley, New York, NY.
Search in Google Scholar
Kaczorek, T. (2002). Positive 1D and 2D Systems, Springer-Verlag, London.10.1007/978-1-4471-0221-2
Search in Google Scholar
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.
Search in Google Scholar
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.
Search in Google Scholar
Kaczorek, T. (2010). Pointwise completeness and pointwise degeneracy of standard and positive linear systems with state-feedbacks, JAMRIS 4(1): 3-7.10.2478/v10170-010-0008-5
Search in Google Scholar
Kaczorek, T. (2011a). Checking of the positivity of descriptor linear systems by the use of the shuffle algorithm, Archives of Control Sciences 21(3): 287-298.10.2478/v10170-010-0044-1
Search in Google Scholar
Kaczorek, T. (2011b). Pointwise completeness and pointwise degeneracy of 2D standard and positive Fornasini-Marchesini models, COMPEL 30(2): 656-670.10.1108/03321641111101131
Search in Google Scholar
Kaczorek, T. (2011c). Reduction and decomposition of singular fractional discrete-time linear systems, Acta Mechanica et Automatica 5(4): 62-66.
Search in Google Scholar
Kaczorek, T. (2011d). Selected Problems of Fractional Systems Theory, Springer-Verlag, Berlin.10.1007/978-3-642-20502-6
Search in Google Scholar
Kaczorek, T. (2011e). Singular fractional discrete-time linear systems, Control and Cybernetics 40(3): 753-761.
Search in Google Scholar
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-2013-0003.10.2478/amcs-2013-0003
Search in Google Scholar
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): 409-412.10.2478/bpasts-2014-0042
Search in Google Scholar
Kaczorek, T. (2014b). Minimum energy control of positive fractional descriptor continuous-time linear systems, IET Control Theory and Applications 8(1): 219-225.10.1049/iet-cta.2013.0362
Search in Google Scholar
Olbrot, A. (1972). On degeneracy and related problems for linear constant time-lag systems, Ricerche di Automatica 3(3): 203-220.
Search in Google Scholar
Popov, V.M. (1972). Pointwise degeneracy of linear time-invariant delay-differential equations, Journal of Differential Equations 11: 541-561.10.1016/0022-0396(72)90066-6
Search in Google Scholar
Trzasko, W., Busłowicz, M. and Kaczorek, T. (2007). Pointwise completeness of discrete-time cone-systems with delays, EUROCON, Warsaw, Poland, pp. 606-611.
Search in Google Scholar
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. 250-262.10.1007/BFb0059944
Search in Google Scholar
Virnik (2008). Stability analysis of positive descriptor systems, Linear Algebra and Its Applications 429(10): 2640-2659. 10.1016/j.laa.2008.03.002
Search in Google Scholar