Geodesic
Transformations of linear standard systems to positive asymptotically stable linear ones
International Journal of Applied Mathematics and Computer Science, Tome 34 (2024) no. 3, pp. 341-348.

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New approaches to transformations of linear continuous-time systems to their positive asymptotically stable canonical controllable (observable) forms are proposed. It is shown that, if the system matrix is nonsingular, then the desired transformation matrix can be chosen in block diagonal form. Procedures for the computation of the transformation matrices are proposed and illustrated with simple numerical examples.
Keywords: asymptotical stability, positive system, continuous time system, linear system
Mots-clés : stabilność asymptotyczna, układ dodatni, układ ciągły dodatni 
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Kaczorek, Tadeusz. Transformations of linear standard systems to positive asymptotically stable linear ones. International Journal of Applied Mathematics and Computer Science, Tome 34 (2024) no. 3, pp. 341-348. http://geodesic.mathdoc.fr/item/IJAMCS_2024_34_3_a0/

[1] Antsaklis, P.J and Michel, A.N. (1997). Linear Systems, Birkhäuser, Boston.

[2] Hautus, M.L.J. and Heymann, M. (1978). Linear feedback - An algebraic approach, SIAM Journal on Control and Optimization 16(1): 83-105.

[3] Gantmacher, F.R. (1959). The Theory of Matrices, Chelsea, London.

[4] Kaczorek, T. (2022). Eigenvalues assignment in uncontrollable linear systems, Bulletin of the Polish Academy of Sciences: Technical Sciences 70(6): 1-3.

[5] Kaczorek, T. (2002). Positive 1D and 2D Systems, Springer, London.

[6] Kaczorek, T. (1992). Linear Control Systems, Vols. 1 and 2, Wiley, New York.

[7] Kaczorek, T. and Borawski, K. (2021). Descriptor Systems of Integer and Fractional Orders, Springer, Cham.

[8] Kaczorek, T. and Rogowski, K. (2015). Fractional Linear Systems and Electrical Circuits, Springer, Cham.

[9] Kailath, T. (1980). Linear Systems, Prentice-Hall, Englewood Cliffs.

[10] Kalman, R.E. (1960). On the general theory of control systems, Proceedings of the IFAC Congress on Automatic Control, Moscow, Soviet Union, pp. 481-492.

[11] Kalman, R.E. (1963). Mathematical description of linear dynamical systems, Journal of the Society for Industrial and Applied Mathematics A: Control 1(2): 152-192.

[12] Klamka, J. (2018). Controllability and Minimum Energy Control, Springer, Cham.

[13] Klamka, J. (1991). Controllability of Dynamical Systems, Kluwer Academic Publishers, Dordrecht.

[14] Mitkowski, W. (2019). Outline of Control Theory, AGH Publishing House, Kraków, (in Polish).

[15] Sajewski, Ł. (2018). Decentralized stabilization of descriptor fractional positive discrete-time linear systems with delays, in R. Szewczyk et al. (Eds), Advances in Automation, Robotics and Measurement Techniques Advances in Intelligent Systems and Computing, Vol. 743, Springer, Cham, pp. 276-287, DOI:10.1007/978-3-319-77179-3_26.

[16] Sajewski, L. (2017) Stabilization of positive descriptor fractional discrete-time linear system with two different fractional orders by decentralized controller, Bulletin of the Polish Academy of Sciences: Technical Sciences 65(5): 709-714.

[17] Zak, S. (2003). Systems and Control, Oxford University Press, New York.