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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.

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