Stabilising slow-switching laws for switched discrete-time linear systems

Author(s): A.-G. Wu ; G. Feng ; G.-R. Duan ; H. Gao
DOI: 10.1049/iet-cta.2010.0643

For access to this article, please select a purchase option:

Buy article PDF

Buy Knowledge Pack

IET members benefit from discounts to all IET publications and free access to E&T Magazine. If you are an IET member, log in to your account and the discounts will automatically be applied.

Learn more about IET membership

Recommend Title Publication to library

IET Control Theory & Applications — Recommend this title to your library

Thank you

Your recommendation has been sent to your librarian.

Author(s): A.-G. Wu ¹ ; G. Feng ² ; G.-R. Duan ³ ; H. Gao ⁴
- Affiliations: 1: Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen, People's Republic of China
  2: Department of Manufacturing Engineering and Engineering Management, City University of Hong Kong, Kowloon, Hong Kong
  3: Center for Control Theory and Guidance Technology, Harbin Institute of Technology, Harbin, People's Republic of China
  4: Space Control and Inertial Technology Research Center, Harbin Institute of Technology, Harbin, People's Republic of China
Source: Volume 5, Issue 16, 3 November 2011, p. 1843 – 1858
DOI: 10.1049/iet-cta.2010.0643 , Print ISSN 1751-8644, Online ISSN 1751-8652

For a class of switched discrete-time linear systems, a state-dependent switching law with dwell time is designed to make the overall system asymptotically stable. A main feature is that the Lyapunov-like function may not be monotonically decreasing in both time-driven and state-driven periods, and this feature allows the proposed stabilising switching law being of lower switching frequency in contrast with recent results. An illustrative example is employed to show the effectiveness of the proposed switching law. Furthermore, it is shown that the proposed switching law ensures that a bounded perturbation implies bounded states, and a convergent perturbation implies convergent states. When the system state is not available, an observer-based state-dependent switching law with dwell time is also developed.

References

1. 1)
  - Fang, L., Lin, H., Antsaklis, P.J.: `Stabilization and performance analysis for a class of switched systems', Proc. 43rd IEEE Conf. on Decision and Control, 2004, Atlantis, USA, p. 3265–3270.
2. 2)
  - E. Feron . (1996) Quadratic stabilizability of switched systems via state and output feedback.
3. 3)
  - Pettersson, S.: `Synthesis of switched linear systems', Proc. 42nd IEEE Conf. on Decision and Control, 2003, p. 5283–5288.
4. 4)
  - A. Bacciotti . Stabilization by means of state space depending switching rules. Syst. Control Lett. , 195 - 201
5. 5)
  - Z. Sun . Combining stabilizing strategies for switched linear systems. IEEE Trans. Autom. Control , 4 , 666 - 674
6. 6)
  - J.C. Geromel , P. Colaner . Stability and stabilization of discrete-time switched systems. Int. J. Control , 7 , 719 - 728
7. 7)
  - T. Hu , L. Ma , Z. Lin . Stabilization of switched systems via composite quadratic functions. IEEE Trans. Autom. Control , 11 , 2571 - 2585
8. 8)
  - Z.G. Li , C.Y. Wen , Y.C. Soh . Stabilization of a class of switched systems via designing switching laws. IEEE Trans. Autom. Control , 4 , 665 - 670
9. 9)
  - M.S. Branicky . Multiple Lyapunov functions and other analysis tools for switched and hybrid systems. IEEE Trans. Autom. Control , 4 , 475 - 482
10. 10)
  - Zhai, G.: `Quadratic stabilizability of discrete-time switched systems via state and output feedback', Proc. 40th IEEE Conf. on Decision and Control, 2001, Orlando, Florida, USA, p. 2165–2166.
11. 11)
  - J.C. Geromel , P. Colaner . Stability and stabilization of continuous-time switched linear systems. SIAM J. Control Optim. , 5 , 1915 - 1930
12. 12)
  - X. Xu , P. Antsaklis . Stabilization of second-order LTI switched systems. Int. J. Control , 14 , 1261 - 1279
13. 13)
  - W. Zhang , A. Abate , J. Hu . Stabilization of discrete-time switched linear systems: a control-Lyapunov function approach. Hybrid Syst.: Comput. Control Lect. Notes Comput. Sci. , 411 - 425
14. 14)
  - Hespanha, J.P., Morse, A.S.: `Stability of switched systems with average dwell-time', Proc. 38th IEEE Conf. on Decision and Control, 1999, p. 2655–2660.
15. 15)
  - Wu, A.G., Feng, G., Zeng, X.: `State feedback stabilizing switching strategies with dwell time for switched discrete-time linear systems', Proc. Eighth World Congress on Intelligence Control and Automation, 2010, Jinan, China, p. 975–980.
16. 16)
  - M.A. Wicks , P. Peleties , R.A. De Carlo . Switched controller synthesis for the quadratic stabilization of a pair of unstable linear systems. Eur. J. Control , 2 , 140 - 147
17. 17)
  - J.S. Chiou , C.M. Cheng . Stabilization analysis of the switched discrete-time systems using Lyapunov stability theorem and genetic algorithm. Chaos Solitons Fractals , 751 - 759
18. 18)
  - X.D. Koutsoukos , P.J. Antsaklis . Design of stabilizing switching control laws for discrete- and continuous-time linear systems using piecewise-linear Lyapunov functions. Int. J. Control , 932 - 945
19. 19)
  - Guisheng, Z., Derong, L., Imae, J., Kobayashi, T.: `Stability analysis for switched systems with continuous-time and discrete-time subsystems: a Lie algebraic approach', Proc. IEEE Int. Symp. Circuits and Systems, 2005, p. 3183–3186.
20. 20)
  - Lin, H., Antsaklis, P.J.: `Switching stabilization and ', Proc. 45th IEEE Conf. on Decision and Control, 2006, San Diego, p. 2673–2678.
21. 21)
  - B. Hu , X. Xu , A.N. Michel , P.J. Antsaklis . Robust stabilizing control laws for a class of second-order switched systems. Syst. Control Lett. , 197 - 207
22. 22)
  - Z. Sun . A robust stabilizing law for switched linear systems. Int. J. Control , 4 , 389 - 398
23. 23)
  - J.P. Hespanha , D. Liberzon , A.S. Morse . Overcoming the limitations of adaptive control by means of logic-based switching. Syst. Control Lett. , 1 , 49 - 65
24. 24)
  - H. Ishii , B.A. Francis . Stabilizing a linear system by switching control with dwell time. IEEE Trans. Autom. Control , 12 , 1962 - 1973
25. 25)
  - G. Zhai , H. Lin , X. Xu , J. Imaea , T. Kobayashia . Analysis of switched normal discrete-time systems. Nonlinear Anal.: Theor. Meth. Appl. , 8 , 1788 - 1799
26. 26)
  - Wicks, M.A., Peleties, P., DeCarlo, R.A.: `Construction of piecewise Lyapunov function for stabilizing switched systems', Proc. IEEE Conf. on Decision and Control, 1994, Lake Buena Vista, USA, p. 3492–3497.
27. 27)
  - Ibeas, A., de la Sen, M., Vilanova, R., Herrera, J.: `Stability of switched linear discrete-time descriptor systems with explicit calculation of a common quadratic Lyapunov sequence', Proc. American Control Conf., 2010, p. 1719–1724.
28. 28)
  - G. Zhai , H. Lin , P.J. Antsaklis . Quadratic stabilizability of switched linear systems with polytopic uncertainties. Int. J. Control , 7 , 747 - 753
29. 29)
  - Pettersson, S., Lennartson, B.: `Stabilization of hybrid systems using a min-projection strategy', Proc. American Control Conf., 2001, Arlington, p. 223–228.
30. 30)
  - Guisheng, Z., Lin, H., Michel, A.N., Yasuda, K.: `Stability analysis for switched systems with continuous-time and discrete-time subsystems', Proc. American Control Conf., 2004, p. 4555–4560.

Stabilising slow-switching laws for switched discrete-time linear systems

Stabilising slow-switching laws for switched discrete-time linear systems

Buy article PDF

Buy Knowledge Pack

Thank you

References

Related content