Geodesic
Stability analysis of nonstationary switched systems
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2020), pp. 63-73

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We investigate the problem of asymptotic stability for nonstationary switched systems. The direct Lyapunov method is used. It is assumed that for any mode a comparison equation in the Bernoulli form is constructed for the considered system. Sufficient conditions on the nonstationary coefficients of the comparison equations and the switching law are found to guarantee the asymptotic stability of the zero solution of the studied system. Obtained results are applied to the stability analysis of some classes of mechanical systems with switched force fields.
Keywords: nonstationary switched systems, asymptotic stability, Lyapunov's direct method. 
@article{IVM_2020_2_a5,
     author = {A. V. Platonov},
     title = {Stability analysis of nonstationary switched systems},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {63--73},
     publisher = {mathdoc},
     number = {2},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2020_2_a5/}
}
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A. V. Platonov. Stability analysis of nonstationary switched systems. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2020), pp. 63-73. http://geodesic.mathdoc.fr/item/IVM_2020_2_a5/