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Partial Eigenvalue Assignment in Discrete-time Descriptor Systems via Derivative State Feedback | ||
| AUT Journal of Modeling and Simulation | ||
| مقاله 4، دوره 48، شماره 2، بهمن 2016، صفحه 65-74 اصل مقاله (1.42 M) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22060/miscj.2016.828 | ||
| نویسندگان | ||
| Sakineh Mirassadi* 1؛ Hojat Ahsani Tehrani2 | ||
| 1Ph.D. Student, Department of Mathematics, Shahrood University of Technology | ||
| 2Associate Professor, Department of Mathematics, Shahrood University of Technology | ||
| چکیده | ||
| A method for solving the descriptor discrete-time linear system is focused. For easily, it is converted to a standard discrete-time linear system by the definition of a derivative state feedback. Then partial eigenvalue assignment is used for obtaining state feedback and solving the standard system. In partial eigenvalue assignment, just a part of the open loop spectrum of the standard linear systems are reassigned, while leaving the rest of the spectrum invariant and for reassigning, similarity transformation is used. Using partial eigenvalue assignment is easier than using eigenvalue assignment. Because by partial eigenvalue assignment, size of matrices and state and input vectors are decreased and stability is kept, too. Also concluding remarks and an algorithm are proposed to the descriptions will be obvious. At the end, convergence of state and input vectors in the descriptor system to balance point (zero) are showed by figures in a numerical example. | ||
| کلیدواژه‌ها | ||
| Descriptor Discrete-Time System؛ Derivative State Feedback؛ Partial Eigenvalue Assignment؛ Converge to Balance Point | ||
| عنوان مقاله [English] | ||
| Partial Eigenvalue Assignment in Discrete-time Descriptor Systems via Derivative State Feedback | ||
| نویسندگان [English] | ||
| Sakineh Mirassadi1؛ Hojat Ahsani Tehrani2 | ||
| 1Ph.D. Student, Department of Mathematics, Shahrood University of Technology | ||
| 2Associate Professor, Department of Mathematics, Shahrood University of Technology | ||
| چکیده [English] | ||
| A method for solving the descriptor discrete-time linear system is focused. For easily, it is converted to a standard discrete-time linear system by the definition of a derivative state feedback. Then partial eigenvalue assignment is used for obtaining state feedback and solving the standard system. In partial eigenvalue assignment, just a part of the open loop spectrum of the standard linear systems are reassigned, while leaving the rest of the spectrum invariant and for reassigning, similarity transformation is used. Using partial eigenvalue assignment is easier than using eigenvalue assignment. Because by partial eigenvalue assignment, size of matrices and state and input vectors are decreased and stability is kept, too. Also concluding remarks and an algorithm are proposed to the descriptions will be obvious. At the end, convergence of state and input vectors in the descriptor system to balance point (zero) are showed by figures in a numerical example. | ||
| کلیدواژه‌ها [English] | ||
| Descriptor Discrete-Time System, Derivative State Feedback, Partial Eigenvalue Assignment, Converge to Balance Point | ||
| مراجع | ||
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[1] Armentano, V. A.; “Eigenvalue Placement for Generalized Linear Systems,” Systems and Control Letter, Vol. 4, No. 4, pp. 199–202, 1984. [2] Bernhard, P.; “On Singular Implicit Linear Dynamical Systems,” SIAM Journal on Control and Optimization, Vol. 20, No. 5, pp. 612–623, 1982. [3] Bunse-Gerstner, A.; Nichols, N. and Mehrmann, V.; “Regularization of Descriptor Systems by Derivative and Proportional State Feedback,” SIAM J. Matrix Anal, Vol. 13, No. 1, pp. 46–67, 1992. [4] Campbell, S. L.; Meyer, C. D. and Rose, N. J.; “Applications of the Drazin Inverse to Linear Systems of Differential Equations with Singular Constant Coefficients,” SIAM Journal on Applied Mathematics, Vol. 31, No. 3, pp. 411–425, 1976.
[5] Cobb, J. D.; “Feedback and Pole Placement in Descriptor Variable Systems,” Int. J. Control, Vol. 33, No. 6, pp. 1135–1146, 1981.
[6] Dai, L.; “Singular Control System,” Lecture Notes in Control and Information Sciences, Springer, Berlin, Vol. 118, 1989.
[7] Datta, B. N.; “Numerical Methods for Linear Control Systems Design and Analysis,” Academic Press, New York, 2002.
[8] Datta, B. N. and Sarkissian, D. R.; “Partial Eigenvalue Assignment in Linear Systems: Existence, Uniqueness and Numerical Solution,” Mathematical Theory of Networks and Systems, Notre Dame, 2002.
[9] Fletcher, L. R.; “Eigenstructure Assignment by Output Feedback in Descriptor Systems,” IEE Proceedings, Vol. 135, No. 4, pp. 302–308, 1988.
[10] Gilnther, M. and Rentrop, P.; “Multirate Row- Methods and Latency of Electric Circuits,” Tech. Rep. TUM-M9208, Mathematisches Inst., Technische Univ. MiJnchen, 1992.
[11] Hopeld, J. J.; “Neural Networks and Physical Systems with Emergent Collective Computational Abilities,” Proc. Natl. Acad. Sci., USA, Vol. 79, No. 8, pp. 2554–2558, 1982.
[12] Kaczorek, T.; “Checking of the Positivity of Descriptor Linear Systems by the Use of the Shuffle Algorithm,” Archives of Control Sciences, Vol. 21, No. 3, pp. 287–298, 2011.
[13] Kaczorek, T.; “Positivity of Descriptor Linear Systems with Regular Pencils,” Archives of Electrical Engineering, Vol. 61, No. 1, pp. 101–113, 2012.
[14] Kaczorek, T.; “Applications of the Drazin Inverse to the Analysis of Descriptor Fractional Discrete-Time Linear Systems with Regular Pencils,” Int. J. Appl. Math. Comput. Sci., Vol. 23, No. 1, pp. 29–33, 2013.
[15] Kaczorek, T.; “Positivity and Asymptotic Stability of Descriptor Linear Systems with Regular Pencils,” Archives of Control Sciences, Vol. 24, No. 2, pp. 193–205, 2014.
[16] Kaczorek, T.; “Analysis of Descriptor Roesser Model with the use of Drazin Inverse,” Int. J. Appl. Math. Comput. Sci., Vol. 25, No. 3, pp. 539–546, 2015.
[17] Karbassi, S. M.; “An Algorithm for Minimizing the Norm of State Feedback Controllers in Eigenvalue Assignment,” Computers and Mathematics with Applications, Vol. 41, No. 10, pp. 1317–1326, 2001.
[18] Karbassi, S. M. and Bell, D. J.; “Parametric Time-Optimal Control of Linear Discrete-Time Systems by State Feedback-Part 1: Regular Kronecker Invariants,” International Journal of Control, Vol. 57, No. 4, pp. 817–830, 1993.
[19] Karbassi, S. M.; and Bell, D. J.; “Parametric Time-Optimal Control of Linear Discrete-Time Systems by State Feedback-Part 2: Irregular Kronecker Invariants,” International Journal of Control, Vol. 57, No. 4, pp. 831–883, 1993.
[20] Lewis, F. L.; “A Survey of Linear Singular Systems,” Circuits Systems Signal Process, Vol. 5, No. 1, pp. 3–36, 1986.
[21] Ozcaldiran, K. and Lewis, F. L.; “A Geometric Approach to Eigenstructure Assignment for Singular Systems,” IEEE, Trans. Automatic Control, Vol. 32, No. 7, pp. 626–632, 1987.
[22] Rahimi, M.; Naserpour, A. and Karbassi, S. M.; “Eigenvalue Assignment in State Feedback Control for Uncertain Systems,” Journal of Scientific Research and Development, Vol. 2, No. 1, pp. 73–75, 2015.
[23] Ramadan, M. A. and El-Sayed, E. A.; “Partial Eigenvalue Assignment Problem of High Order Control Systems Using Orthogonality Relations,” Computers and Mathematics with Applications, Vol. 59, No. 6, pp. 1918–1928, 2010.
[24] Saad, Y.; “Projection and Deflation Methods for Partial Pole Assignment in Linear State Feedback,” IEEE Trans. Automat. Control, Vol. 33, No. 3, pp. 290–297, 1988.
[25] Schmidt, T. and Hou, M.; “Bollringgetriebel,” Internal Rep., Sicherheitstechnische Regelungsund MeBtechnik, Bergische Univ., GH Wuppertal, Wuppertal, FRG, 1992.
[26] Varga, A.; “On stabilization Methods of Descriptor Systems,” Systems and Control Letters, Vol. 24, No. 2, pp. 133–138, 1995.
[27] Zhai, G. and Xu, X.; “A Unified Approach to Stability Analysis of Switched Linear Descriptor Systems under Arbitrary Switching,” Int. J. Apple. Math. Comput. Sci., Vol. 20, No. 2, pp. 249–259, 2010.
[28] Zhoua, L. and Lub, G.; “Detection and Stabilization for Discrete-Time Descriptor Systems via a Limited Capacity,” Atomtica, Vol. 45, No. 10, pp. 2272–2277, 2009. | ||
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