Finite-Time Control for Switched Discrete-Time System

Abstract:

Finite-time stability concerns the boundless of system during a fixed finite-time interval. In this paper, the problem of finite-time stabilization for switched discrete-time systems is addressed. Both the fast switching and slow switching case are considered. In fast switching case, the designed state feedback controller combines controllers for each subsystem and resetting controller at switching instant, it is shown that the resetting controller can reduce the conservativeness on controller design. Under slow switching, state feedback controller is designed with admissible average dwell time. Several numerical examples are given to illustrate the proposed results within this paper.

• Periodical: Applied Mechanics and Materials (Volumes 313-314)
• Pages: 516-523
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.313-314.516
• Online since: March 2013
• Authors: Wei Ming Xiang, Yong Chi Zhao
• Keywords: Average Dwell Time, Finite-Time Stability, Finite-Time Stabilization, Switched Discrete-Time Systems

References

[1] L. Weiss and E. Infante, "Finite time stability under perturbing forces and on product spaces", IEEE Transactions on Automatic Control, vol. 12, no.1, p.54–59, 1967.

DOI: 10.1109/tac.1967.1098483

[2] A. N. Michel and S. H. Wu. "Stability of discrete systems over a finite interval of time", International Journal of Control, vol. 9, no. 6, p.679– 693, 1969.

DOI: 10.1080/00207176908905789

[3] H. D'Angelo, Linear Time-Varying Systems: Analysis and Synthesis, Boston, MA: Allyn and Bacon, 1970.

[14] F. Amato, M. Ariola and C. Cosentino, "Finite-time stabilization via dynamic output feedback", Automatica, 41, p.337–342, 2006.

DOI: 10.1016/j.automatica.2005.09.007

[5] F. Amato and M. Ariola, "Finite-time control of discrete-time linear systems", IEEE Transactions on Automatic Control, vol. 50, no. 5, p.724–729, 2005.

DOI: 10.1109/tac.2005.847042

[6] A. Balluchi, M. D. Benedetto, C. Pinello, C. Rossi, and A. Sangiovanni–Vincentelli, "Cut-off in engine control: a hybrid system approach", in Proceedings of the 36th IEEE Conference on Decision and Control, 1997, p.4720–4725.

DOI: 10.1109/cdc.1997.649753

[7] B. E. Bishop and M. W. Spong, "Control of redundant manipulators using logic-based switching", in Proceedings of the 36th IEEE Conference on Decision and Control, 1998, p.16–18.

DOI: 10.1109/cdc.1998.758498

[8] W. Zhang, M. S. Branicky and S.M. Phillips, "Stability of networked control systems", IEEE Control Systems Magazine, 2001, vol. 21, no. 1, p.84–99.

[9] K. S. Narendra and J. A. Balakrishnan, "Common Lyapunov function for stable LTI systems with commuting A-matrices", IEEE Transactions on Automatic Control, vol. 39, no. 12, p.2469–2471, 1994.

DOI: 10.1109/9.362846

[10] M. S. Branicky, "Multiple Lyapunov functions and other analysis tools for switched and hybrid systems", IEEE Transactions on Automatic Control, vol. 43, no. 4, p.475–482, 1998.

DOI: 10.1109/9.664150

[11] H. Ye, A. N. Michel and L. Hou, "Stability theory for hybrid dynamic systems", IEEE Transactions on Automatic Control, vol. 43, no. 4, p.461–474, 1998.

DOI: 10.1109/9.664149

[12] J. P. Hespanha, D. Liberzon and A. S. Morse, "Stability of switched systems with average dwell time", in Proceedings of 38th Conference on Decision and Control, 1999, p.2655–2660.

DOI: 10.1109/cdc.1999.831330

[13] H. Lin and P. J. Antsaklis, "Stability and stabilizability of switched linear systems: a survey of recent results", IEEE Transactions on Automatic Control, vol. 54, no. 2, p.308–322, 2009.

DOI: 10.1109/tac.2008.2012009