Stability of interval positive continuous-time linear systems

• Autorzy: Kaczorek T.

Identyfikatory

DOI

10.24425/119056

• Języki publikacji: EN

Abstrakty

EN

It is shown that the convex linear combination of the Hurwitz polynomials of positive linear systems is also the Hurwitz polynomial. The Kharitonov theorem is extended to the positive interval linear systems. It is also shown that the interval positive linear system described by state equation x ̇ = Ax, A ϵ ℜ^n×n, A1 ≥ A ≤ A2 is asymptotically stable if and only if the matrices A_k = 1, 2 are Hurwitz Metzler matrices.

Słowa kluczowe

EN

interval; positive; linear; continuous-time; system; stability

PL

interwał; system; stabilność

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 2018
• Tom: Vol. 66, nr 1
• Strony: 31--35
• Opis fizyczny: Bibliogr. 25 poz.

Twórcy

autor

Kaczorek T.

• Białystok University of Technology, Faculty of Electrical Engineering

Bibliografia

• [1] T. Kaczorek, “Positive fractional continuous-time linear systems with singular pencils”, Bull. Pol. Ac.: Tech. 60 (1), 9‒1 (2012).
• [2] T. Kaczorek, Positive 1D and 2D Systems, Springer-Verlag, London, 2000.
• [3] T. Kaczorek, “Analysis of positivity and stability of fractional discrete-time nonlinear systems”, Bull. Pol. Ac.: Tech. 64 (3), 491‒494 (2016).
• [4] T. Kaczorek, “Analysis of positivity and stability of discrete-time and continuous-time nonlinear systems”, Computational Problems of Electrical Engineering 5 (1), (2015).
• [5] T. Kaczorek, “Descriptor positive discrete-time and continuous-time nonlinear systems”, Proc. of SPIE, vol. 9290 (2014).
• [6] T. Kaczorek, “Positivity and stability of discrete-time nonlinear systems”, IEEE 2nd International Conference on Cybernetics, 156‒159 (2015).
• [7] T. Kaczorek, “Stability of fractional positive nonlinear systems”, Archives of Control Sciences, 25 (4), 491‒496 (2015).
• [8] M. Busłowicz, “Stability analysis of continuous-time linear systems consisting of n subsystems with different fractional orders”, Bull. Pol. Ac.: Tech. vol. 60, no. 2, 2012, 279‒284.
• [9] T. Kaczorek, “Fractional positive continuous-time linear systems and their reachability”, Int. J. Appl. Math. Comput. Sci. 18 (2), 223‒228 (2008).
• [10] T. Kaczorek, “Positive linear systems with different fractional orders”, Bull. Pol. Ac.: Tech. 58 (3), 453‒458 (2010).
• [11] T. Kaczorek, “Positive linear systems consisting of n subsystems with different fractional orders”, IEEE Trans. on Circuits and Systems, 58 (7), 1203‒1210 (2011).
• [12] Ł. Sajewski, “Descriptor fractional discrete-time linear system with two different fractional orders and its solution”, Bull. Pol. Ac.: Tech. 64 (1), 15‒20 (2016).
• [13] W. Xiang-Jun, W. Zheng-Mao, and L. Jun-Guo, “Stability analysis of a class of nonlinear fractional-order systems”, IEEE Trans. Circuits and Systems-II, Express Briefs, 55 (11), 1178‒118 (2008).
• [14] T. Kaczorek, “Positive singular discrete-time linear systems”, Bull. Pol. Ac.: Tech. 45 (4), 619‒631 (1997).
• [15] 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 (1), 29‒34 (2013).
• [16] H. Zhang, D. Xie, H. Zhang, and G. Wang, “Stability analysis for discrete-time switched systems with unstable subsystems by a mode-dependent average dwell time approach”, ISA Transactions, 53, 1081‒1086 (2014).
• [17] J. Zhang, Z. Han, H. Wu, and J. Hung, “Robust stabilization of discrete-time positive switched systems with uncertainties and average dwell time switching”, Circuits Syst. Signal Process., 33, 71‒95 (2014).
• [18] Ł. Sajewski, “Descriptor fractional discrete-time linear system and its solution – comparison of three different methods”, Challenges in Automation, Robotics and Measurement Techniques, Advances in Intelligent Systems and Computing, vol. 440, 2016, 37‒50.
• [19] M. Busłowicz, “Stability of linear continuous-time fractional order systems with delays of the retarded type”, Bull. Pol. Ac.: Tech. 56 (4), 319‒324 (2008).
• [20] M. Busłowicz and T. Kaczorek, “Simple conditions for practical stability of positive fractional discrete-time linear systems”, Int. J. Appl. Math. Comput. Sci. 19 (2), 263‒169 (2009).
• [21] L. Farina and S. Rinaldi, Positive Linear Systems; Theory and Applications, J. Wiley, New York, 2000.
• [22] T. Kaczorek, “Positivity and stability of standard and fractional descriptor continuous-time linear and nonlinear systems”, Int. J. of Nonlinear Sciences and Num. Simul. (2017) (in press)
• [23] A. Berman and R.J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, SIAM, 1994.
• [24] T. Kaczorek, Theory of Control and Systems, PWN, Warszawa, 1993 (in Polish).
• [25] V.L. Kharitonov, “Asymptotic stability of an equilibrium position of a family of systems of differential equations”, Differentsialnye uravneniya, 14, 2086‒2088 (1978).

Uwagi

PL

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