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STABILITY OF SOLUTIONS TO ONE CLASS DISCONTINUOUS SYSTEMS

Annotation

We give spectral conditions for stability and instability of solutions to one class of quasilinear nonautonomous systems of differential equations with discontinuous right-hand sides. The results obtained do not use the Lyapunov functions.

Keywords

stability; spectral method; normal matrix

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UDC

517.925

Pages

1730-1735

References

1. Andronov A.A., Vitt A.A., Khaykin S.E. Teoriya kolebaniy. M.: Fizmatgiz, 1959. 2. Gelig A.Kh., Leonov G.A., Yakubovich V.A. Ustoychivost' nelineynykh sistem s needinstvennym sostoyaniem ravnovesiya. M.: Nauka, 1978. 3. Demidovich B.P. Lektsii po matematicheskoy teorii ustoychivosti. M.: Nauka, 1967. 4. Krasovskiy N.N., Subbotin A.I. Pozitsionnye differentsial'nye igry. M.: Nauka, 1974. 5. Filippov A.F. Differentsial'nye uravneniya s razryvnoy pravoy chast'yu. M.: Nauka, 1985. 6. Chezari L. Asimptoticheskoe povedenie i ustoychivost' resheniy obyknovennykh differentsial'nykh urav- neniy. M.: Mir, 1964. 7. Bezyaev V.I., Konyaev Yu.A. Analiz ustoychivosti resheniy odnogo klassa kvazilineynykh neavtonomnykh razryvnykh sistem // Vestnik RUDN. Seriya: Matematika. Informatika. Fizika. Moskva, 2010. № 4. S. 5-10.

Received

2015-09-16

Section of issue

Mathematics

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