Abstract
The positivity of discrete-time and continuous-time nonlinear systems is addressed. Necessary and sufficient conditions for the positivity of the descriptor nonlinear systems are established. A procedure for checking the positivity is proposed and demonstrated on numerical examples.
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References
Bru, R., Coll, C., Romero-Vivo, S., Sanchez, E.: Some problems about structural properties of positive descriptor systems. In: Benvenuti, L., De Santis, A., Farina, L. (eds.) Positive Systems. (LNCIS), vol. 294, pp. 233–240. Springer, Berlin (2003).10.1007/978-3-540-44928-7_32
Bru, R., Coll, C., Sanchez, E.: About positively discrete-time singular systems. In: System and Control: Theory and Applications, Electrical & Computer Engineering Series, pp. 44–48. World Scientific and Engineering Academy and Society, Athens (2000)
Bru, R., Coll, C., Sanchez, E.: Structural properties of positive linear time-invariant difference-algebraic equations. Linear Algebra Appl. 349, 1–10 (2002)
Campbell, S.L., Meyer, C.D., Rose, N.J.: Applications of the Drazin inverse to linear systems of differential equations with singular constructions. SIAM J. Appl. Math. 31(3), 411–425 (1976)
Commalut, C., Marchand, N.: Positive Systems. Lecture Notes in Control and Information Science, vol. 341. Springer, Berlin (2006)
Dai, L.: Singular control systems. Lectures Notes in Control and Information Sciences. Springer, Berlin (1989)
Dodig, M., Stosic, M.: Singular systems state feedbacks problems. Linear Algebra Appl. 431(8), 1267–1292 (2009)
Fahmy, M.M., O’Reill, J.: Matrix pencil of closed-loop descriptor systems: infinite-eigenvalues assignment. Int. J. Control 49(4), 1421–1431 (1989)
Farina, L., Rinaldi, S.: Positive Linear Systems. Wiley, New York (2000)
Gantmacher, F.R.: The Theory of Matrices. Chelsea Publishing Co., New York (1960)
Kaczorek, T.: Checking of the positivity of descriptor linear systems with singular pencils. Arch. Control Sci. 22(1), 77–86 (2012)
Kaczorek, T.: Infinite eigenvalue assignment by output-feedbacks for singular systems. Int. J. Appl. Math. Comput. Sci. 14(1), 19–23 (2004)
Kaczorek, T.: Linear Control Systems, vol. 1. Wiley, New York (1992)
Kaczorek, T.: Polynomial and Rational Matrices: Applications in Dynamical Systems Theory. Springer, London (2007)
Kaczorek, T.: Positive 1D and 2D Systems. Springer, London (2002)
Kaczorek, T.: Positive linear systems with different fractional orders. Bull. Pol. Acad. Sci. Techn. 58(3), 453–458 (2010)
Kaczorek, T.: Positivity of descriptor linear systems with regular pencils. Arch. Electr. Eng. 61(1), 101–113 (2012)
Kaczorek, T.: Positivity and asymptotic stability of descriptor linear systems with regular pencils. Arch. Control Sci. 24(2), 193–205 (2014)
Kaczorek, T.: Realization problem for singular positive continuous-time systems with delays. Control Cybern. 36(1), 47–57 (2007)
Kaczorek, T.: Selected Problems of Fractional Systems Theory. Springer, Berlin (2011)
Kaczorek, T.: Stability of descriptor positive linear systems. COMPEL - Int. J. Comput. Math. Electr. Electron. Eng. 32(1), 412–423 (2013)
Kucera, V., Zagalak, P.: Fundamental theorem of state feedback for singular systems. Automatica 24(5), 653–658 (1988)
Van Dooren, P.: The computation of Kronecker’s canonical form of a singular pencil. Linear Algebra Appl. 27, 103–140 (1979)
Virnik, E.: Stability analysis of positive descriptor systems. Linear Algebra Appl. 429, 2640–2659 (2008)
Acknowledgment
This work was supported by National Science Centre in Poland under work No. 2014/13/B/ST7/03467.
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Kaczorek, T. (2017). Descriptor Positive Nonlinear Systems. In: Szewczyk, R., Zieliński, C., Kaliczyńska, M. (eds) Automation 2017. ICA 2017. Advances in Intelligent Systems and Computing, vol 550. Springer, Cham. https://doi.org/10.1007/978-3-319-54042-9_3
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DOI: https://doi.org/10.1007/978-3-319-54042-9_3
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