Abstract
Descriptor observers for descriptor discrete-time linear systems are investigated. Two different methods of observer synthesis are analyzed and the comparison of the methods is performed. The methods are based on: [Ez–A]−1 expansion and Weierstrass-Kronecker decomposition. Considerations are illustrated by numerical examples.
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References
Campbell, S.L., Meyer, C.D., Rose, N.J.: Applications of the Drazin inverse to linear systems of differential equations with singular constant coefficients. SIAMJ Appl. Math. 31(3), 411–425 (1976)
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)
Guang-Ren, D.: Analysis and Design of Descriptor Linear Systems. Springer, New York (2010)
Fahmy, M.M., O’Reilly, J.: Matrix pencil of closed-loop descriptor systems: infinite-eigenvalues assignment. Int. J. Control 49(4), 1421–1431 (1989)
Kaczorek, T.: Descriptor fractional linear systems with regular pencils. Asian J. Control 15(4), 1051–1064 (2013)
Kaczorek, T.: Fractional descriptor observers for fractional descriptor continuous-time linear systems. Arch. Control Sci. 24(1), 27–37 (2014)
Kaczorek, T.: Infinite eigenvalue assignment by output-feedback for singular systems. Int. J. Appl. Math. Comput. Sci. 14(1), 19–23 (2004)
Kaczorek, T.: Linear Control Systems, vol. 1. Research Studies Press, J. Wiley, New York (1992)
Kaczorek, T.: Minimum energy control of descriptor positive discrete-time linear systems. COMPEL 33(3), 976–988 (2014)
Kaczorek, T.: Minimum energy control of positive fractional descriptor continuous-time linear systems. IET Control Theor. Appl. 8(4), 219–225 (2013)
Kaczorek, T.: Reduced-order fractional descriptor observers for a class of fractional descriptor continuous-time nonlinear systems. Int. J. Appl. Math. Comput. Sci. 26(2), 277–283 (2016)
Kaczorek, T.: Positive fractional continuous-time linear systems with singular pencils. Bull. Pol. Acad. Sci. Techn. 60(1), 9–12 (2012)
Kaczorek, T.: Reduced-order fractional descriptor observers for fractional descriptor continuous-time linear systems. Bull. Pol. Acad. Sci. Techn. 62(4), 889–895 (2014)
Kaczorek, T.: Vectors and Matrices in Automation and Electrotechnics. WNT, Warsaw (1998)
Kaczorek, T., Borawski, K.: Fractional descriptor continuous-time linear systems described by the Caputo-Fabrizio derivative. Int. J. Appl. Math. Comput. Sci. 26(3), 533–541 (2016)
Kaczorek, T., Borawski, K.: Minimum energy control of descriptor discrete-time linear systems by the use of Weierstrass-Kronecker decomposition. Arch. Control Sci. 26(2), 177–187 (2016)
Kucera, V.: Observer-based deadbeat controllers: a polynomial design. Kybernetika 16(5), 431–441 (1980)
Kucera, V., Zagalak, P.: Fundamental theorem of state feedback for singular systems. Automatica 24(5), 653–658 (1988)
Sajewski, Ł.: Descriptor fractional discrete-time linear system and its solution—comparison of three different methods. In: Szewczyk, R., Zieliński, C., Kaliczyńska, M. (eds.) Challenges in Automation, Robotics and Measurement Techniques. AISC, vol. 440, pp. 37–50. Springer, Heidelberg (2016). doi:10.1007/978-3-319-29357-8_4
Sajewski, Ł.: Solution of the state equation of descriptor fractional continuous-time linear systems with two different fractional orders. Adv. Intell. Syst. Comput. 350, 233–242 (2015)
Valcher, M.E., Willems, J.C.: Dead beat observer synthesis. Syst. Control Lett. 37, 285–292 (1999)
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(10), 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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Borawski, K. (2017). Comparison of Two Different Methods of Observer Synthesis for Descriptor Discrete-Time Linear 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_14
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DOI: https://doi.org/10.1007/978-3-319-54042-9_14
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