Denysenko V. The conditions of stability of the nonlinear mechanical systems established on basis of locally-linear approximations

Українська версія

Thesis for the degree of Candidate of Sciences (CSc)

State registration number

0410U000229

Thesis Registration Form

0410U000229.pdf

Applicant for

Specialization

  • 01.02.01 - Теоретична механіка

26-01-2010

Specialized Academic Board

Д 26.166.01

S.P.Timoshenko Institute of Mechanics

Essay

The thesis is devoted to establishing of a new conditions of stability of the nonlinear mechanical systems, the motion's equations of which are obtained on basis of locally-linear approximations by Takagi-Sugeno models. The sufficient conditions of asymptotic and exponential stability of zero solution of continuous, discrete and impulsive locally-linear systems are established. Also the sufficient conditions of robust stability of linear impulsive systems are obtained. These conditions are expressed as some restrictions on system's parameters. On the basis of obtained theoretical results the stability of stationary motions of some mechanical systems and one task of mathematical biology are investigated.

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