Finite-time stability of switched nonlinear systems with finite-time unstable subsystems.

*(English)*Zbl 1307.93192Summary: Up to now, the precondition that each subsystem should be finite-time stable or finite-time bounded is potentially assumed in most existing results for finite-time stability and finite-time boundedness of switched systems. If one subsystem of switched systems is not finite-time stable or finite-time bounded, the previous results may not work. In this paper, based on Lyapunov-like functions, finite-time stability and finite-time boundedness problems of switched nonlinear systems with subsystems that are not finite-time stable or finite-time bounded are discussed. Sufficient conditions are given under which switched nonlinear systems with subsystems that are finite-time unstable or finite-time unbounded are guaranteed to be still finite-time stable or finite-time bounded by virtue of Lyapunov-like functions respectively. The results also show the effect of switching signals and the total dwell time of finite-time unstable or finite-time unbounded subsystems on finite-time stability and finite-time boundedness of switched nonlinear systems. Numerical examples are employed to verify the efficiency of the proposed method.

##### MSC:

93C30 | Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems) |

93C10 | Nonlinear systems in control theory |

93D30 | Lyapunov and storage functions |

93D99 | Stability of control systems |

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\textit{X. Li} et al., J. Franklin Inst. 352, No. 3, 1192--1214 (2015; Zbl 1307.93192)

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