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Journal Articles IEEE Transactions on Automatic Control Year : 2021

Conditions of self-oscillations in generalized Persidskii systems


For a class of generalized Persidskii systems, whose dynamics are described by superposition of a linear part with multiple sector nonlinearities and exogenous perturbations, the conditions of practical stability, instability and oscillatory behavior in the sense of Yakubovich are established. For this purpose the conditions of local instability at the origin and global boundedness of solutions (practical input-to-state stability) are developed in the form of linear matrix inequalities. The proposed theory is applied to investigate robustness to unmodeled dynamics of nonlinear feedback controls in linear systems, and to determine the presence of oscillations in the models of neurons.


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hal-03168417 , version 1 (13-03-2021)



Jian Wang, Jésus Mendoza Avila, Denis Efimov, Alexander Yu Aleksandrov, Leonid Fridman. Conditions of self-oscillations in generalized Persidskii systems. IEEE Transactions on Automatic Control, 2021, ⟨10.1109/TAC.2021.3066581⟩. ⟨hal-03168417⟩
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