Research Papers

Finite-Time Input-to-State Stability and Optimization of Switched Nonlinear Systems

[+] Author and Article Information
Xiaoli Wang

e-mail: xiaoliwang@amss.ac.cn

Chuntao Shao

e-mail: chtshaw@gmail.comSchool of Information and Electrical Engineering, Harbin Institute of Technology at Weihai, Shandong, Weihai 264209, China

Contributed by the Dynamic Systems Division of ASME for publication in the Journal of Dynamic Systems, Measurement, and Control. Manuscript received December 29, 2011; final manuscript received March 1, 2013; published online May 27, 2013. Assoc. Editor: Sergey Nersesov.

J. Dyn. Sys., Meas., Control 135(4), 041018 (May 27, 2013) (5 pages) Paper No: DS-11-1410; doi: 10.1115/1.4024006 History: Received December 29, 2011; Revised March 01, 2013

In this paper, we address the (uniform) finite-time input-to-state stability problem for switched nonlinear systems. We prove that a switched nonlinear system has a useful finite-time input-to-state stability property under average dwell-time switching signals if each constituent subsystem has finite-time input-to-state stability. Moreover, we prove the equivalence between the optimal costs for the switched nonlinear systems and for the relaxed differential inclusion.

Copyright © 2013 by ASME
Your Session has timed out. Please sign back in to continue.


Bengea, S., and DeCarlo, R., 2005, “Optimal Control of Switching Systems,” Automatica, 41(1), pp. 11–27. [CrossRef]
Mancilla-Aguilar, J. L., and Garcia, R. A., 2000, “A Converse Lyapunov Theorem for Nonlinear Switched Systems,” Syst. Control Lett., 41, pp. 67–71. [CrossRef]
Mancilla-Aguilar, J. L., and Garcia, R. A., 2001, “A Converse Lyapunov Theorems for ISS and iISS Switched Nonlinear Systems,” Syst. Control Lett., 42, pp. 47–53. [CrossRef]
Zhang, L., Chen, Y., and Cui, P., 2005, “Stabilization for a Class of Second-Order Switched Systems,” Nonlinear Anal., 62, pp. 1527–1535. [CrossRef]
Sun, Z., 2006, “Stabilization and Optimization of Switched Linear Systems,” Automatica, 42, pp. 783–788. [CrossRef]
Bhat, S., and Bernstein, D., 2000, “Finite-Time Stability of Continuous Autonomous Systems,” SIAM J. Control Optim., 38, pp. 751–766. [CrossRef]
Orlov, Y., 2005, “Finite-Time Stability and Robust Control Synthesis of Uncertain Switched Systems,” SIAM J. Control Optim., 43, pp. 1253–1271. [CrossRef]
Wang, X., and Hong, Y., 2008, “Finite-Time Consensus for Multi-Agent Networks With Second-Order Agent Dynamics,” Proceedings of theIFAC World Congress, pp. 15185–15190. [CrossRef]
Ryan, E., 1991, “Finite-Time Stabilization of Uncertain Nonlinear Planar Systems,” Dyn. Control, 1, pp. 83–94. [CrossRef]
Xu, J., Sun, J., and Yue, D., 2012, “Stochastic Finite-Time Stability of Nonlinear Markovian Switching Systems With Impulsive Effects,” ASME J. Dyn. Sys., Meas., Control, 134(1), p. 011011. [CrossRef]
Sontag, E. D., and Wang, Y., 1995, “On Characterizations of the Input to State Stability Property,” Syst. Control Lett., 24, pp. 351–359. [CrossRef]
Sontag, E. D., 2000, “The ISS Philosophy as a Unifying Framework for Stability-Like Behavior,” Nonlinear Control in the Year 2000, Lecture Notes in Control and Information Sciences, A.Isidori, F.Lamnabhi-Lagarrigue, and W.Respondek, eds., Springer-Verlag, Berlin, pp. 443–468.
Lin, Y., Sontag, E. D., and Wang, Y., 1996, “A Smooth Converse Lyapunov Theorem for Robust Stability,” SIAM J. Control Optim., 34(1), pp. 124–160. [CrossRef]
Hong, Y., Jiang, Z. P., and Feng, G., 2010, “Finite-Time Input-to-State Stability and Applications to Finite-Time Control Design,” SIAM J. Control Optim.48, pp. 4395–4418. [CrossRef]
Xie, W., Wen, C., and Li, Z., 2001, “Input-to-State Stabilization of Switched Nonlinear Systems,” IEEE Trans. Autom. Control, 46, pp. 1111–1116. [CrossRef]
Vu, L., Chatterjee, D., and Liberzon, D., 2007, “Input-to-State Stability of Switched Systems and Switching Adaptive Control,” Automatica, 43, pp. 639–646. [CrossRef]
Kartsatos, A., 1980, Advanced Ordinary Differential Equations, Mariner, Tampa, FL.
Yoshizawa, T., 1966, “Stability Theory by Lyapunov Second Method.” J. Math. Soci. Jpn., 9, pp. 521–535.
Aubin, J. P., and Cellina, A., 1984, Differential Inclusions, Springer-Verlag, Berlin.




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In