Partial stability analysis of some classes of nonlinear systems |
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| Authors: | Alexander ALEKSANDROV Elena ALEKSANDROVA Alexey ZHABKO Yangzhou CHEN |
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| Institution: | Saint Petersburg State University, Saint Petersburg 199034, Russia;Beijing Key Laboratory of Transportation Engineering, College of Metropolitan Transportation, Beijing University of Technology, Beijing 100124, China |
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| Abstract: | 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. |
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| Keywords: | Nonlinear systems partial asymptotic stability Lyapunov function sector nonlinearities time-delay 34D20 34K20 93D30 |
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