Asymptotic and exponential stability of certain third-order non-linear delayed differential equations: frequency domain method
The asymptotic stability of the zero solution for some third order delayed differential equations is studied by the frequency domain method. Also, for the non-homogeneous equations, the existence of exponentially stable bounded solutions is proved. The known theorems on absolute stability for the system of the form \[ \dot X(t)=AX(t)+BX(t-\tau)-Q\varphi(\sigma(t))+P(t),\quad \sigma(t)=C_1X(t)+C_2X(t) \] with sector conditions for \(\varphi\) are used to obtain the results.
scientific article; zbMATH DE number 5707074
scientific article