Positive time-varying continuous-time linear systems and electrical circuits

• Autorzy: Kaczorek T.

Identyfikatory

DOI

10.1515/bpasts-2015-0095

• Języki publikacji: EN

Abstrakty

EN

The positivity of time-varying continuous-time linear systems and electrical circuits are addressed. Necessary and sufficient conditions for the positivity of the systems and electrical circuits are established. It is shown that there exists a large class of positive electrical circuits with time-varying parameters. Examples of positive electrical circuits are presented.

Słowa kluczowe

EN

linear; time-varying system; electrical circuit; stability test; system

PL

test stabilności; obwód elektryczny; 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 4
• Strony: 837--842
• Opis fizyczny: Bibliogr. 25 poz., rys.

Twórcy

autor

Kaczorek T.

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

Bibliografia

• [1] L. Farina and S. Rinaldi, Positive Linear Systems; Theory and Applications, J. Wiley, New York, 2000.
• [2] T. Kaczorek, Positive 1D and 2D Systems, Springer Verlag, London, 2002.
• [3] A. Czornik and M. Niezabitowski, “On the stability of Lyapunov exponents of discrete linear system”, Proc. Eur. Control Conf. 1, 2210-2213 (2013).
• [4] A. Czornik, A. Newrat, M. Niezabitowski, and A. Szyda, “On the Lyapunov and Bohl exponent of time-varying discrete linear systems”, 20th Mediterranean Conf. on Control and Automation (MED) 1, 194-197 (2012).
• [5] A. Czornik and M. Niezabitowski, “Lyapunov exponents for systems with unbounded coefficients”, Dynamical Systems: Int. J. 28 (2), 140-153 (2013).
• [6] A. Czornik, A. Newrat, and M. Niezabitowski, “On the Lyapunov exponents of a class of the second order discrete time linear systems with bounded perturbations”, Dynamical Systems: Int. J. 28 (4), 473-483 (2013).
• [7] A. Czornik and M. Niezabitowski, “On the stability of discrete time-varying linear systems”, Nonlinear Analysis: Hybrid Systems 9, 27-41 (2013).
• [8] A. Czornik, J. Klamka, and M. Niezabitowski, “On the set of Perron exponents of discrete linear systems”, Proc. World Congress 19th Int. Federation Automatic Control 1, 11740-11742 (2014).
• [9] T. Kaczorek, “Positivity and stability of fractional descriptor time-varying discrete-time linear systems”, AMCS, (2015), (to be published).
• [10] T. Kaczorek, “Positive descriptor time-varying discrete-time linear systems and their asymptotic stability”, Trans Nav. Int. J. Marine Navigation and Safety Sea Transportation 9 (1), 83-89 (2015).
• [11] T. Kaczorek, “Positivity and stability of time-varying discretetime linear systems”, in Intelligent Information and Database Systems. Lecture Notes in Computer Science, pp. 295-303, Springer, Lausanne, 2015.
• [12] T. Kaczorek, “Fractional standard and positive descriptor timevarying discrete-time linear systems”, Conf. Automation 1, CDROM (2015).
• [13] T. Kaczorek, “Stability and stabilization of positive fractional linear systems by state-feedbacks”, Bull. Pol. Ac:. Tech. 58 (4), 517-554 (2010).
• [14] T. Kaczorek, “Stability of positive continuous-time linear systems with delays”, Bull. Pol. Ac:. Tech. 57 (4), 395-398 (2009).
• [15] T. Kaczorek, ‘Positive and stable time-varying continuous-time linear systems and electrical circuits”, Academic J. Poznan Univ. Technology 81, 11-19 (2015).
• [16] T. Kaczorek, “Fractional positive continuous-time linear systems and their reachability”, Int. J. Appl. Math. Comput. Sci. 18 (2), 223-228 (2008).
• [17] T. Kaczorek, “Positivity and reachability of fractional electrical circuits”, Acta Mechanica et Automatica 5 (2), 42-51 (2011).
• [18] T. Kaczorek, Selected Problems of Fractional System Theory, Springer, Berlin, 2011.
• [19] T. Kaczorek, “New stability tests of positive standard and fractional linear systems”, Circuits and Systems 2, 261-268 (2011).
• [20] T. Kaczorek, “Positive linear systems consisting of n subsystems with different fractional orders”, IEEE Trans. Circuits and Systems 58 (6), 1203-1210.
• [21] T. Kaczorek, “Positive electrical circuits and their reachability”, Archives of Electrical Engineering 60 (2), 283-301 (2011).
• [22] T. Kaczorek, “Controllability and observability of linear electrical circuits”, Electrical Review 87, 248-254 (2011).
• [23] T. Kaczorek, “Normal positive electrical circuits”, IET Control Theory and Applications, doi: 10.1049/iet-cta.2014.0183 (2014).
• [24] T. Kaczorek, Vectors and Matrices in Automation and Electrotechnics, WNT, Warszawa, 1998.
• [25] F.R. Gantmacher, The Theory of Matrices, Chelsea Pub. Comp., London, 1959.