Geodesic
On the existence and construction of common Lyapunov functions for switched discrete systems
Sibirskij žurnal industrialʹnoj matematiki, Tome 21 (2018) no. 4, pp. 75-85

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Under consideration is the problem of stability of switched discrete systems with the generalized homogeneous right-hand sides. The conditions are obtained for the existence of the common Lyapunov function, and a method for its construction is proposed in the form of a combination of the partial Lyapunov functions obtained for isolated subsystems. For a special case of linear three-dimensional systems, some algorithms are proposed for constructing common Lyapunov functions as quadratic and fourth degree forms. Some examples illustrate the effectiveness of the proposed approach.
Keywords: switched discrete system, stability, common Lyapunov function. 
@article{SJIM_2018_21_4_a5,
     author = {A. A. Kosov and M. V. Kozlov},
     title = {On the existence and construction of common {Lyapunov} functions for switched discrete systems},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {75--85},
     publisher = {mathdoc},
     volume = {21},
     number = {4},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2018_21_4_a5/}
}
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A. A. Kosov; M. V. Kozlov. On the existence and construction of common Lyapunov functions for switched discrete systems. Sibirskij žurnal industrialʹnoj matematiki, Tome 21 (2018) no. 4, pp. 75-85. http://geodesic.mathdoc.fr/item/SJIM_2018_21_4_a5/