Exponential stability in a scalar functional differential equation

Exponential Stability in a Scalar Functional Differential Equation

We establish a criterion for the global exponential stability of the zero solution of the scalar retarded functional differential equation x (t) = L(x t) + g(t,x t) whose linear part y (t) = L(y t) generates a monotone semiflow on the phase space C = C([−r,0],R) with respect to the exponential ordering, and the nonlinearity g has at most linear growth.

Exponential stability for a nonlinear functional differential equation

A Global Stability Criterion for Scalar Functional Differential Equations

We consider scalar delay differential equations x′(t) = −δx(t)+f(t, xt) (∗) with nonlinear f satisfying a sort of negative feedback condition combined with a boundedness condition. The well-known Mackey–Glass-type equations, equations satisfying the Yorke condition, and equations with maxima all fall within our considerations. Here, we establish a criterion for the global asymptotical stability...

Exponential stability for a class of functional differential equations

The pth moment exponential stability of multifactor uncertain differential equation

In this paper, we mainly introduced a definition of moment exponential stability for multifactor uncertain differential equation. For illustrating of stability concept, several examples and counterexamples are given. Furthermore, a necessary and sufficient condition of stability in pth moment exponential of linear multifactor uncertain differential equation is obtained. Also, the necessary and ...