Geodesic
Positive invertibility of matrices and exponential stability of impulsive systems of Ito linear differential equations with bounded delays
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2020), pp. 18-35

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Based on the theory of inverse-positive matrices, some problems of exponential $2p$–stability $(1 \le p \infty )$ of systems of linear differential Ito equations with bounded delays and impulse effects on the part of the solution components are investigated. The ideas and methods developed by N.V. Azbelev and his students to study deterministic stability of functional dfferential equations are applied. For the above mentioned systems of equations, suffcient conditions for exponential $2p$-stability ($(1 \le p \infty )$ are given in terms of positive invertibility of matrices constructed via the parameters of these systems. Feasibility of these conditions is checked for speciffic systems of equations.
Mots-clés : Ito equations
Keywords: stability of solutions, impulse effects, positive invertibility of matrices, bounded delays. 
@article{IVM_2020_8_a2,
     author = {R. I. Kadiev and A. V. Ponosov},
     title = {Positive invertibility of matrices and exponential stability of impulsive systems of {Ito} linear differential equations with bounded delays},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {18--35},
     publisher = {mathdoc},
     number = {8},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2020_8_a2/}
}
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R. I. Kadiev; A. V. Ponosov. Positive invertibility of matrices and exponential stability of impulsive systems of Ito linear differential equations with bounded delays. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2020), pp. 18-35. http://geodesic.mathdoc.fr/item/IVM_2020_8_a2/