Geodesic
Connectivity estimations of errors of linearization of essentially nonlinear systems
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2013), pp. 51-63

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We consider a nonlinear dynamical system with several connectivity components. It includes subsystems which can be switched off or on in the operation process, i.e., the system undergoes structural changes. It is well-known that such systems are stable with respect to the connectivity. This property is known as the connectivity stability. In this paper we find an upper bound for the solution of the initial multiply-connected domain of a nonlinear dynamical system and obtain a connectivity estimation for its linearization error.
Keywords: asymptotic stability, Lyapunov vector function, connectivity estimation of the linearization error. 
@article{IVM_2013_11_a3,
     author = {A. V. Shchennikov and V. N. Shchennikov},
     title = {Connectivity estimations of errors of linearization of essentially nonlinear systems},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {51--63},
     publisher = {mathdoc},
     number = {11},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2013_11_a3/}
}
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A. V. Shchennikov; V. N. Shchennikov. Connectivity estimations of errors of linearization of essentially nonlinear systems. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2013), pp. 51-63. http://geodesic.mathdoc.fr/item/IVM_2013_11_a3/