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Stability of discontinuous nonlinear singular systems

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Abstract

This paper studies a class of nonlinear singular systems with discontinuous right-hand sides, it develops nonsmooth Lyapunov stability theory as well as LaSalle invariance principle. In this paper, LaSalle invariance principle of the discontinuous nonlinear singular systems is presented firstly. Furthermore, some sufficient conditions for stability and asymptotic stability of the given systems based on Filippov differential inclusion and Clarke’s generalized gradient are given. Finally, these results are illustrated by the given example.

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Correspondence to Xiaowu Mu.

Additional information

This research is supported by the National Natural Science Fundation of China under Grant No. 60874006.

This paper was recommended for publication by Editor TIAN Yuping.

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Wei, J., Mu, X. Stability of discontinuous nonlinear singular systems. J Syst Sci Complex 26, 527–533 (2013). https://doi.org/10.1007/s11424-013-1189-3

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  • DOI: https://doi.org/10.1007/s11424-013-1189-3

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