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Asymptotic and exponential stability of certain third-order non-linear delayed differential equations: frequency domain method. (English) Zbl 1200.34081

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

X ˙(t)=AX(t)+BX(t-τ)-Qϕ(σ(t))+P(t),σ(t)=C 1 X(t)+C 2 X(t)

with sector conditions for ϕ are used to obtain the results.

34K20Stability theory of functional-differential equations
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