TY - JOUR

T1 - Partial stability analysis of some classes of nonlinear systems

AU - ALEKSANDROV, Alexander

AU - ALEKSANDROVA, Elena

AU - ZHABKO, Alexey

AU - CHEN, Yangzhou

PY - 2017/3/1

Y1 - 2017/3/1

N2 - A nonlinear differential equation system with nonlinearities of a sector type is studied. Using the Lyapunov direct method and the comparison method, conditions are derived under which the zero solution of the system is stable with respect to all variables and asymptotically stable with respect to a part of variables. Moreover, the impact of nonstationary perturbations with zero mean values on the stability of the zero solution is investigated. In addition, the corresponding time-delay system is considered for which delay-independent partial asymptotic stability conditions are found. Three examples are presented to demonstrate effectiveness of the obtained results.

AB - A nonlinear differential equation system with nonlinearities of a sector type is studied. Using the Lyapunov direct method and the comparison method, conditions are derived under which the zero solution of the system is stable with respect to all variables and asymptotically stable with respect to a part of variables. Moreover, the impact of nonstationary perturbations with zero mean values on the stability of the zero solution is investigated. In addition, the corresponding time-delay system is considered for which delay-independent partial asymptotic stability conditions are found. Three examples are presented to demonstrate effectiveness of the obtained results.

KW - Lyapunov function

KW - Nonlinear systems

KW - partial asymptotic stability

KW - sector nonlinearities

KW - time-delay

UR - http://www.scopus.com/inward/record.url?scp=85013914378&partnerID=8YFLogxK

U2 - 10.1016/S0252-9602(17)30005-X

DO - 10.1016/S0252-9602(17)30005-X

M3 - Article

AN - SCOPUS:85013914378

VL - 37

SP - 329

EP - 341

JO - Acta Mathematica Scientia

JF - Acta Mathematica Scientia

SN - 0252-9602

IS - 2

ER -