Reachability and observability of positive discrete-time linear systems with integer positive and negative powers of the state Frobenius matrices

• Autorzy: Kaczorek T.

Identyfikatory

DOI

10.24425/119080

• Języki publikacji: EN

Abstrakty

EN

The notions of monomial generalized Frobenius matrices is proposed and the reachability and observability of positive discrete-time linear systems with positive and negative integer powers of the state matrices is addressed. Necessary and sufficient conditions for the reachability of the positive systems are established.

Słowa kluczowe

EN

discrete-time; linear; positive; system; monomial Frobenius generalized matrix; reachability; observability

• Wydawca: Polish Academy of Sciences, Committee of Automatic Control and Robotics
• Czasopismo: Archives of Control Sciences
• Rocznik: 2018
• Tom: Vol. 28, No. 1
• Strony: 119--133
• Opis fizyczny: Bibliogr. 23 poz., wzory

Twórcy

autor

Kaczorek T.

• Białystok University of Technology, Faculty of Electrical Engineering, Wiejska 45D, 15-351 Białystok, Poland

Bibliografia

• [1] Bru R., Coll C., Romero-Vivo S. and Sanchez E.: 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] Bru R., Coll C. and Sanchez E.: 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] Bru R., Coll C. and Sanchez E.: Structural properties of positive linear time-invariant difference-algebraic equations, Linear Algebra Appl., 349, (2002), 1-10.
• [4] Farina L. and Rinaldi S.: Positive Linear Systems; Theory and Applications, J. Wiley, New York, 2000.
• [5] Kaczorek T.: Analysis of positivity and stability of discrete-time and continuous-time nonlinear systems, Computational Problems of Electrical Engineering, 5(1), (2015).
• [6] Kaczorek T.: Checking of the positivity of descriptor linear systems by the use of the shuffle algorithm, Archives of Control Sciences, vol. 21(3), (2011), 287-298.
• [7] Kaczorek T.: Descriptor positive discrete-time and continuous-time nonlinear systems, Proc. of SPIE, 9290, doi:10.1117/12.2074558.
• [8] Kaczorek T.: Descriptor standard and positive discrete-time nonlinear systems, Automatyzacja Procesów Dyskretnych, 1, (2014), 113-120.
• [9] Kaczorek T.: Minimum energy control of descriptor positive discrete-time linear systems, COMPEL, 33(3), (2014), 976-988.
• [10] Kaczorek T.: Minimum energy control of fractional descriptor positive discrete-time linear systems, Int. J. Appl.Math. Comput. Sci., 24(4), (2014), 735-743.
• [11] Kaczorek T.: Minimum energy control of positive fractional descriptor continuous-time linear systems, Control Theory & Applications IET, 8(4), (2014), 215-225.
• [12] Kaczorek T.: Necessary and sufficient conditions for minimum Energy control of positive discrete-time linear systems with bounded inputs, Bull. Pol. Acad. Sci. Tech., 62(1), (2014), 85-89.
• [13] Kaczorek T.: Positive linear systems with different fractional orders, Bull. Pol. Acad. Sci. Tech., 58(3), (2010), 453-458.
• [14] Kaczorek T.: Positive 1D and 2D Systems, Springer-Verlag, London, 2002.
• [15] Kaczorek T.: Positive descriptor discrete-time linear systems, Problems of Nonlinear Analysis in Engineering Systems, 1(7), (1998), 38-54.
• [16] Kaczorek T.: Positive linear systems consisting of n subsystems with different fractional orders, IEEE Trans. Circuits and Systems, 58(6), (2011), 1203-1210.
• [17] Kaczorek T.: Positive singular discrete-time linear systems, Bull. Pol. Acad. Sci. Tech., 45(4), (1997), 619-631.
• [18] Kaczorek T.: Positivity and linearization of a class of nonlinear discrete-time systems by state feedbacks, Logistyka, 6, (2014), 5078-5083.
• [19] Kaczorek T.: Positivity and stability of discrete-time nonlinear systems, IEEE 2nd International Conference on Cybernetics, 2015, 156-159.
• [20] Kaczorek T. and Borawski K.: Stability of continuous-time and discrete-time linear systems with inverse state matrices, Measurement Automation Monitoring, 62(4), (2016), 132-135.
• [21] Kaczorek T. and Ostalczyk P.: Positivity and stability of fractional discrete-time systems. The model without a time shift in the difference, Control and Cybernetics, 46(1), (2017).
• [22] Kaczorek T. and Rogowski K.: Fractional Linear Systems and Electrical Circuits, Studies in Systems, Decision and Control, 13, Springer, 2015.
• [23] Virnik E.: Stability analysis of positive descriptor systems, Linear Algebra and its Applications, 429, 2640-2659.

Uwagi

EN

This work was supported by National Science Centre in Poland under work No. 2014/13/B/ST7/03467.

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).