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

• Autorzy: Kaczorek T.

Identyfikatory

DOI

10.1515/bpasts-2015-0019

• Języki publikacji: EN

Abstrakty

EN

Pointwise completeness and pointwise degeneracy of the fractional descriptor continuous-time linear systems with regular pencils are addressed. Conditions for the pointwise completeness and pointwise degeneracy of the systems are established and illustrated by an example.

Słowa kluczowe

EN

pointwise completeness; pointwise degeneracy; descriptor; fractional; continuous-time; linear; system

PL

punktowa kompletność; punktowa degeneracja; deskryptor; czas ciągły; liniowość; system

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 2015
• Tom: Vol. 63, nr 1
• Strony: 169--–172
• Opis fizyczny: Bibliogr. 27

Twórcy

autor

Kaczorek T.

• Faculty of Electrical Engineering, Bialystok University of Technology, 45D Wiejska St., 15-351 Bialystok, Poland

Bibliografia

• [1] R. Bru, C. Coll, S. Romero-Vivo, and E. Sanchez, “Some problems about structural properties of positive descriptor systems”, Lecture Notes in Control and Inform. Sci. 294, 233-240 (2003).
• [2] R. Bru, C. Coll, and E. Sanchez, “Structural properties of positive linear time-invariant difference-algebraic equations”, Linear Algebra Appl. 349, 1-10 (2002).
• [3] S.L. Campbell, C.D. Meyer, and N.J. Rose, “Applications of the Drazin inverse to linear systems of differential equations with singular constant coefficients”, SIAMJ Appl. Math. 31, 411-425 (1976).
• [4] L. Dai, Singular Control Systems, Springer-Verlag, Berlin, 1989.
• [5] Guang-Ren Duan, Analysis and Design of Descriptor Linear Systems, Springer, New York, 2010.
• [6] T. Kaczorek, “Application of Drazin inverse to analysis of descriptor fractional discrete-time linear systems with regular pencils”, Int. J. Appl. Math. Comput. Sci. 23, 29-33 (2013).
• [7] T. Kaczorek, “Checking of the positivity of descriptor linear systems by the use of the shuffle algorithm”, Archives of Control Sciences 21, 287-298 (2011).
• [8] T. Kaczorek, “Drazin inverse matrix method for fractional descriptor continuous-time linear systems”, Bull. Pol. Ac.: Tech. 62, 409-412 (2014).
• [9] T. Kaczorek, “Infinite eigenvalue assignment by outputfeedbacks for singular systems”, Int. J. Appl. Math. Comput. Sci. 14, 19-23 (2004).
• [10] T. Kaczorek, Linear Control Systems, vol. 1, Research Studies Press J. Wiley, New York, 1992.
• [11] T. Kaczorek, “Minimum energy control of positive fractional descriptor continuous-time linear systems”, IET Control Theory and Applications, doi:10.1049/oet-cta.2013.0362, 1-7 (2013).
• [12] T. Kaczorek, “Reduction and decomposition of singular fractional discrete-time linear systems”, Acta Mechanica et Automatica 5, 62-66 (2011).
• [13] T. Kaczorek, “Singular fractional discrete-time linear systems”, Control and Cybernetics 40, 753-761 (2011).
• [14] E. Virnik, “Stability analysis of positive descriptor systems”, Linear Algebra and Its Applications 429, 2640-2659 (2008).
• [15] T. Kaczorek, Selected Problems of Fractional Systems Theory, Springer-Verlag, Berlin, 2011.
• [16] T. Kaczorek, Positive 1D and 2D Systems, Springer-Verlag, London, 2002.
• [17] M. Busłowicz, “Pointwise completeness and pointwise degeneracy of linear discrete-time systems of fractional order”, Automatics. Notebooks of the Silesian University of Technology 151, 19-24 (2008), (in Polish).
• [18] M. Busłowicz, R. Kociszewski, and W. Trzasko, “Pointwise completeness and pointwise degeneracy of positive discrete-time systems with delays”, Automatics. Notebooks of the Silesian University of Technology 145, 51-56 (2006), (in Polish).
• [19] A.K. Choudhury, “Necessary and sufficient conditions of pointwise completeness of linear time-invariant delay-differential systems”, Int. J. Control 16, 1083-1100 (1972).
• [20] T. Kaczorek and M. Busłowicz, “Pointwise completeness and pointwise degeneracy of linear continuous-time fractional order systems”, J. Automation, Mobile Robotics & Intelligent Systems 3, 8-11 (2009).
• [21] T. Kaczorek, “Pointwise completeness and pointwise degeneracy of 2D standard and positive Fornasini-Marchesini models”, COMPEL 30, 656-670 (2011).
• [22] T. Kaczorek, “Pointwise completeness and pointwise degeneracy of standard and positive fractional linear systems with statefeedbacks”, Archives of Control Sciences 19, 295-306 (2009).
• [23] T. Kaczorek, “Pointwise completeness and pointwise degeneracy of standard and positive linear systems with statefeedbacks”, JAMRIS 4, 3-7 (2010).
• [24] A. Olbrot, “On degeneracy and related problems for linear constant time-lag systems”, Ricerche di Automatica 3, 203-220 (1972).
• [25] V.M. Popov, “Pointwise degeneracy of linear time-invariant delay-differential equations”, J. Diff. Equation 11, 541-561 (1972).
• [26] W. Trzasko, M. Busłowicz, and T. Kaczorek, “Pointwise completeness of discrete-time cone-systems with delays”, Proc. EUROCON 1, 606-611 (2007).
• [27] L. Weiss, “Controllability for various linear and nonlinear systems models”, Lecture Notes in Mathematics 144, Seminar on Differential Equations and Dynamic System II, 250-262 (1970).