Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 30178
LMI Approach to Regularization and Stabilization of Linear Singular Systems: The Discrete-time Case

Authors: Salim Ibrir

Abstract:

Sufficient linear matrix inequalities (LMI) conditions for regularization of discrete-time singular systems are given. Then a new class of regularizing stabilizing controllers is discussed. The proposed controllers are the sum of predictive and memoryless state feedbacks. The predictive controller aims to regularizing the singular system while the memoryless state feedback is designed to stabilize the resulting regularized system. A systematic procedure is given to calculate the controller gains through linear matrix inequalities.

Keywords: Singular systems, Discrete-time systems, Regularization, LMIs

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1076932

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1234

References:


[1] F. L. Lewis, "A survey of linear singular systems," Circuit syst., Signal Processing, vol. 5, pp. 3-36, 1986.
[2] L. Dai, Singular control systems. Springer, 1989, vol. 118, lecture Notes in Control and Information sciences.
[3] F. N. Koumboulis and B. G. Mertzios, "On kalman-s controllability and observability criteria for singular systems," Circuit syst., Signal Processing, vol. 18, no. 3, pp. 269-290, 1999.
[4] J. Yoshiyuki and M. H. Terra, "On the lyapunov theorem for singular systems," IEEE Transactions on Automatic Control, vol. 47, no. 11, pp. 1926-1930, 2002.
[5] D. Wang and C. B. Soh, "On regularizing singular systems by decentralized output feedback," IEEE Transactions on Automatic Control, vol. 44, no. 1, pp. 148-152, 1999.
[6] K. O┬¿ zc┬©aldiran and F. L. Lewis, "On the regularizability of singular systems," IEEE Transactions on Automatic Control, vol. 35, no. 10, pp. 1156-1160, 1990.
[7] D. Chu and D. y. Cai, "Regularization of singular systems by output feedback," Journal of computational mathematics, vol. 18, no. 1, pp. 43-60, 2000.
[8] D. Chu, V. Mehrmann, and N. K. Nichols, "Minimum norm regularization of discriptor systems by mixed output feedback," Linear algebra and its applications, vol. 296 , pp. 39-77, 1999.
[9] A. Bunce-Gerstner, R. Byers, V. Mehrmann, and N. K. Nicols, "Feedback design for regularizing descriptor systems," Linear algebra and its applications, vol. 299, pp. 119-151, 1999.
[10] L. Dai, "Observers for discrete singular systems," IEEE Transactions on Automatic Control, vol. 33, no. 2, pp. 187-191, 1988.
[11] ÔÇöÔÇö, "Filtering and lqg problems for discrete-time stochastic singular systems," IEEE Transactions on Automatic Control, vol. 34, no. 10, pp. 1105-1108, 1989.
[12] S. Ibrir, "Linear time-derivative trackers," Automatica, vol. 40, no. 3, pp. 397-405, 2004.