Positive fractional continuous-time linear systems with singular pencils

• Autorzy: Kaczorek T.
• Języki publikacji: EN

Abstrakty

EN

A method for checking the positivity and finding the solution to the positive fractional descriptor continuous-time linear systems with singular pencils is proposed. The method is based on elementary row and column operations of the fractional descriptor systems to equivalent standard systems with some algebraic constraints on state variables and inputs. Necessary and sufficient conditions for the positivity of the fractional descriptor systems are established.

Słowa kluczowe

EN

positive; fractional; descriptor; continuous-time; linear; system; singular pencil

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 2012
• Tom: Vol. 60, nr 1
• Strony: 9--12
• Opis fizyczny: Bibliogr. 17 poz., rys., tab.

Twórcy

autor

Kaczorek T.

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

Bibliografia

• [1] C. Commalut and N. Marchand, Positive Systems, vol. 341, Springer-Verlag, Berlin, 2006.
• [2] T. Kaczorek, Positive 1D and 2D Systems, Springer-Verlag, London, 2002.
• [3] L. Farina and S. Rinaldi, Positive Linear Systems, J. Willey, New York, 2000.
• [4] S.L. Campbell, Singular Systems of Differential Equations, vol. 40, Pitman Advanced Publishing Program, Boston, 1980.
• [5] S.L. Campbell, C.D. Meyer, and N.J. Rose, “Applications of the Drazin inverse to linear systems of differential equations with singular constructions”, SIAMJ Appl. Math. 31 (3), 411–425 (1976).
• [6] M.P. Drazin, “Pseudo-inverses in associative rings and semigroups”, Amer. Math. Monthly 65, 506–514 (1958).
• [7] L. Dai, Singular Control Systems, vol. 118, Springer-Verlag, Berlin, 1989.
• [8] T. Kaczorek, Linear Control Systems, vol. 1, Research Studies Press and J. Wiley, New York, 1992.
• [9] 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).
• [10] R. Bru, C. Coll, and E. Sanchez, “About positively discretetime singular systems”, System and Control: Theory and Applications, Electr. Comput. Eng. Ser., World Sci. Eng. Soc. Press 1, 44–48 (2000).
• [11] R. Bru, C. Coll, and E. Sanchez, “Structural properties of positive linear time-invariant difference-algebraic equations”, Linear Algebra Appl. 349, 1–10 (2002).
• [12] T. Kaczorek, “Checking of the positivity of descriptor linear systems by the use of the shuffle algorithm”, Archives of Control Sciences 21, CD-ROM (2011).
• [13] T. Kaczorek, “Singular fractional linear systems and electrical circuits”, Int. J. Appl. Math. Comput. Sci. 21 (2), 379–384 (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 System Theory, Springer-Verlag, Berlin 2011.
• [16] T. Kaczorek, “Positive fractional 2D continuous-discrete linear systems”, Bull. Pol. Ac.: Tech. 59 (4), 575–580 (2011).
• [17] T. Kaczorek, “Stability and stabilization of positive fractional systems by state-feedbacks”, Bull. Pol. Ac.: Tech. 58 (4), 537–554 (2010).