Geodesic
Finite-time boundedness and stabilization of switched linear systems
Kybernetika, Tome 46 (2010) no. 5, pp. 870-889

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In this paper, finite-time boundedness and stabilization problems for a class of switched linear systems with time-varying exogenous disturbances are studied. Firstly, the concepts of finite-time stability and finite-time boundedness are extended to switched linear systems. Then, based on matrix inequalities, some sufficient conditions under which the switched linear systems are finite-time bounded and uniformly finite-time bounded are given. Moreover, to solve the finite-time stabilization problem, stabilizing controllers and a class of switching signals are designed. The main results are proven by using the multiple Lyapunov-like functions method, the single Lyapunov-like function method and the common Lyapunov-like function method, respectively. Finally, three examples are employed to verify the efficiency of the proposed methods.
Classification : 93A14, 93C10, 93D15, 93D21
Keywords: switched linear systems; finite-time boundedness; multiple Lyapunov-like functions; single Lyapunov-like function; common Lyapunov-like function 
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     author = {Du, Haibo and Lin, Xiangze and Li, Shihua},
     title = {Finite-time boundedness and stabilization of switched linear systems},
     journal = {Kybernetika},
     pages = {870--889},
     publisher = {mathdoc},
     volume = {46},
     number = {5},
     year = {2010},
     mrnumber = {2778923},
     zbl = {1205.93076},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2010__46_5_a4/}
}
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Du, Haibo; Lin, Xiangze; Li, Shihua. Finite-time boundedness and stabilization of switched linear systems. Kybernetika, Tome 46 (2010) no. 5, pp. 870-889. http://geodesic.mathdoc.fr/item/KYB_2010__46_5_a4/