H∞ control and input-to-state stabilization for hybrid systems with time delay

Abstract

This paper addresses the problem of designing a robust reliable H∞ control and a switching law to guarantee input-to-state stabilization (ISS)for a class of uncertain switched control systems with time delay not only when all the actuators are operational, but also when some of them experience failure. The output of faulty actuators are treated as a disturbance signal that is augmented with the system disturbance input. Multiple Lyapunov functionwith Razumikhin technique, and average dwell-time switching signal are used to establish the ISS property

Keywords

• Switched systems, ISS, robust reliable H1control, multiple Lyapunovfunctions, average dwell time, time delay

References

1. Alwan, M.S., Liu, X.Z., and Xie, W.-C., On design of robust reliable H1control and input-to-state stabilization of uncertain stochastic systems with state delay. Communications in Nonlinear Science and Numerical Simu., vol. 18, no. 4, pp. 1047-1056, 2013.
2. Chen, G. and Xiang, Z., Robust reliable H1control of switched stochastic sys- tems with time delays under asynchronous switching, Advances in Diğerential Equations, a Springer Open Journal, article no. 86, 2013.
3. Cheng, X.M, Gui, W.H., and Gan, Z.J., Robust reliable control for a class of time-varying uncertain impulsive systems. Journal of Central South University Technology, vol. 12, no. 1, pp. 199-202, 2005.
4. Gao, J., Huang, B., Wang, Z., and Fisher, D.G., Robust reliable control for a class of uncertain nonlinear systems with time-varying multi-state time delays, International Journal of Systems Sciences, vol. 32, no. 7, pp. 817-824, 2001.
5. Khalil, H.K., Nonlinear systems, 3rd Edition. Prentice-Hall, 2002. [6] Kuang, Y., Delay diğerential equations with applications in population dy- namics. Academic press, INC. Mathematics in science and engineering, vol. 191, 1993.
6. Liberzon, D., Switching in Systems and Control. Birkhäuser, 2003.
7. Liberzon, D. and Morse, A.S., Basic Problems is Stability and Design of Switched Systems. IEEE Control Systems Magazine, vol. 19, no.5, pp. 59-70, 1999.
8. Lu, J. and Wu, Z., Robust reliable H1control for uncertain switched linear sys- tems with disturbances. 2nd int. conference (ICIECS), IEEE Xplore, December, 2010.

9. Luo, X., Yang, L., Yang, H., and Guan, X., Robust reliable control for neutral delay systems, Proceedings of the 6th World Congress on Intelligent Control and Automation, June 21-23, Dalian, China, pp. 144-148, 2006.
10. Seo, C.J. and Kim, B.K., Robust and reliable H1control for linear systems with parameter uncertainty and actuator failure. Automatica, vol. 32, no. 3, pp. 465-467, 1996.
11. Shorten, R., Wirth, F., Mason, O., Wulğ K., and King C., Stability criteria for switched and hybrid systems. SIAM Review, vol. 49, no. 4, pp. 545, 2007.
12. Sontag, E.D., Smooth stabilization implies coprime factorization, IEEE Trans actions on Automatic Control, vol. 34, no. 4, pp. 435-443, 1989.
13. Teel, A.R., Moreau, L., and Nešic, D., A note on the robustness of ISS stability.
14. Proceeding of the 40th IEEE on decision and control, Florida, pp. 875-880, 2001.
15. Veillette, R.J., Medanic, J.V., and Perkins, W.R., Design of reliable control systems. IEEE Transactions on Automatic Control, vol. 37, no. 3, pp. 290-304, 1992.
16. Wang, J., and Shao, H., Delay-dependent robust and reliable H1control for uncertain time-delay systems with actuator failurs, Journal of the Franklin Institute, vol. 337, pp. 781-791, 2000.
17. Xu, S., and Chen, T., Robust H1control for uncertain stochastic systems with state delay, IEEE Transaction on Automatic Control, vol. 47, no. 12, pp. 2089-2094, 2002.
18. Yang, G.H., Wang, J.L., and Soh Y.C., Reliable H1control design for linear systems. Automatica, vol. 37, no. 5, pp. 717-725, 2001.