Checking of the positivity of descriptor linear systems with singular pencils

• Autorzy: Kaczorek T.
• Języki publikacji: EN

Abstrakty

EN

A method for checking of the positivity of descriptor continuous-time and discrete-time linear systems with singular pencil is proposed. The method is based on elementary row and column operations on the matrices of descriptor systems. Necessary and sufficient conditions for the positivity of the descriptor systems are established.

Słowa kluczowe

EN

checking; positivity; descriptor; linear systems; singular pencil

• Wydawca: Polish Academy of Sciences, Committee of Automatic Control and Robotics
• Czasopismo: Archives of Control Sciences
• Rocznik: 2012
• Tom: Vol. 22, no. 1
• Strony: 77--86
• Opis fizyczny: Bibliogr. 14 poz., wzory

Twórcy

autor

Kaczorek T.

• Faculty of Electrical Engineering, Bialystok University of Technology, Wiejska 45D, 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. Positive systems (Rome, 2003), Lecture Notes in Control and Inform. Sci. 294 Springer, Berlin, 2003, 233-240.
• [2] R. Bru, C. Coll and E. Sanchez: About positively discrete-time singular systems, System and Control: theory and applications. Electr. Comput. Eng. Ser., World Sci. Eng. Soc. Press, Athens, (2000), 44-48.
• [3] R. Bru, C. Coll and E. Sanchez: Structural properties of positive linear time-invariant difference-algebraic equations. Linear Algebra Appl., 349 (2002), 1-10.
• [4] S. L. Campbell: Singular Systems of Differential Equations. Research Notes in Mathematics, 40 Pitman (Advanced Publishing Program), Boston, Mass., (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 constant coefficients. SIAMJ Appl. Math., 31(3), (1976), 411-425.
• [6] C. Commalut and N. Marchand, (EDS.): Positive Systems. Lecture Notes in Control and Inform. Sci., 341 Springer-Verlag, Berlin, 2006.
• [7] L. Dai: Singular Control Systems. Lecture Notes in Control and Inform. Sci., 118 Springer-Verlag, Berlin, 1989.
• [8] M. P. Drazin: Pseudo-inverses in associative rings and semigroups. Amer. Math. Monthly, 65 1958, 506-514.
• [9] L. Farina and S. Rinaldi: Positive Linear Systems. J. Willey, New York, 2000.
• [10] T. Kaczorek: Positive 1D and 2D Systems. Springer-Verlag, London 2002.
• [11] T. Kaczorek: Linear Control Systems. 1 Research Studies Press and J. Wiley, New York 1992.
• [12] T. Kaczorek: Selected Problems of Fractional System. Theory. Springer-Verlag, Berlin 2011.
• [13] T. Kaczorek: Checking of the positivity of descriptor linear systems by the use of the shuffle algorithm. Archives of Control Sciences, 21(3), (2011), 287-298.
• [14] E. Virnik: Stability analysis of positive descriptor systems. Linear Algebra and its Applications, 429 (2008), 2640-2659.