Pole Assignment Of Linear Discrete-Time Periodic Systems In Specified Discs Through State Feedback

Document Type : Research Article

Author

Assistant Professor, Department of Mathematics, Shahrood University, Shahrood, Iran

Abstract

The problem of pole assignment, also known as an eigenvalue assignment, in linear discrete-time periodic systems in discs was solved by a novel method which employs elementary similarity operations. The former methods tried to assign the points inside the unit circle while preserving the stability of the discrete time periodic system. Nevertheless, now we can obtain the location of eigenvalues in the specified discs, randomly. An illustrative example with random system matrices is presented in order to show the effectiveness of the method.

Keywords


[1] F.A. Aliev, C.C. Arcasoy, V.B. Larin, and N.A.Safarova, “Synthesis problem for periodic systems
by static output feedback,” Applied and Computational Mathematics. vol 4(2),pp. 102–113, 2005.
[2] F.A. Aliev, C.C. Arcasoy, V.B. Larin, and N.A.Safarova, “Synthesis problem for periodic systems
by static output feedback,” Applied and Computational Mathematics. vol 4(2),pp. 102–113, 2005.
[3] P. Benner, M. Castillo, and E.S Quintana-orti,“Partial stabilization of large-scale discrete-time
linear control systems,” Technical Report,University of Bremen, Germany. March 2001.
[4] J. H. Chou, “Pole assignment robustness in a specified disk,” Systems & Control Letters, vol 16, pp. 41-44, 1991.
[5] C. Farges, D. Peaucelle, and D. Arzelier,” Resilient static output feedback stabilization of linear periodic systems,” In: 5th IFAC Symposium on Robust Control Design, Toulouse 2006.
[6] C. Farges, D. Peaucelle, D. Arzelier, and J. Daafouz, “Robust performance analysis and synthesis of linear polytopic discrete-time periodic systems via LMIs,” Systems & Control Letters, vol 56(2), pp. 159.166, 2007.
[7] M. M. Fateh, H. Ahsani Tehrani, and S. M. Karbassi, “Repetitive control of electrically driven robot manipulators,” International Journal of Systems Science, Published Online: 18 Oct 2011.
[8] J. L. Figueroa and J. A. Romagnoli, “An algorithm for robust pole assignment via polynomial approach,” IEEE Transactions on Automatic Control, vol 39,pp. 831-835,1994.
[9] K. Furuta and S. B. Kim, “Pole assignment in a specified disk,” IEEE Transactions on Automatic Control, vol 32, pp. 423-427, 1987.
[10] L. Grammont and A. Largillier, “Krylov method revisited with an application to the localization of eigenvalues ,” Numerical Functional Analysis and Optimization, vol 27, pp. 583-618,
[11] G. Guo, J.F. Qiao, and C.Z. Han, “Controllability of periodic systems: continuous and discrete,” in proc IEE Control Theory and Applications, vol 151, pp. 488-490, 2004.
[12] S.M. Karbassi and D.J. Bell, “Parametric time-optimal control of linear discrete-time systems by state feedback-Part 1: Regular Kronecker invariants,” International Journal of Control, vol. 57, pp. 817-830, 1993.
[13] S.M. Karbassi and D.J. Bell, “Parametric time-optimal control of linear discrete-time systems by state feedback-Part 2: Irregular Kronecker invariants,” International Journal of Control, vol 57, pp. 831-839,1993.
[14] S.M. Karbassi and H.A. Tehrani, “Parameterizations of the state feedback controllers for linear multivariable systems ,” Computers and Mathematics with Applications, vol 44, pp. 1057-1065, 2002.
[15] B.P. Lampe and E. N. Rossenwasser, “Closed formulae for the L2-norm of linear continuous-time periodic systems ,” In: Proc. PSYCO, 231-236, Japan 2004.
[16] B.P. Lampe, M. A. Obraztso, and E. N. Rosenwasser, “Statistical analysis of stable
FDLCP systems by parametric transfer matrices ,” International Journal of Control, vol 78(10), pp. 747-761, 2005.
[17] S. Longhi, and R. Zulli, “A note on robust pole assignment for periodic systems,” IEEE Transactions on Automatic Control, vol 41, pp. 1493-1497, 1996.
[18] C.E.De. Souza and A. Trono, “An LMI approach to stabilization of linear discrete-time periodic systems,” International Journal of Control, vol 73, pp. 696-703, 2000.
[19] A. Varga, “Computation of l-infinity norm of linear discrete-time periodic systems,” In: Proc. MTNS 2006.
[20] J. Zhou and T. Hagiwara, “H2 and H-infinity norm computations of linear continuous-time periodic systems via the skew analysis of frequency response operators,” Automatica, vol 38, pp. 1381-1387, 2002.