In this paper, new delay-independent asymptotic and exponential stability conditions of linear discrete delay systems based on the LyapunovKrasovskii method have been derived. A numerical example has been developed so as to show applicability of the derived results.

We consider the inverse scattering problem on the energy interval in three dimensions. We are focused on stability and instability questions for this problem. In particular, we prove an exponential instability estimate which shows optimality of the logarithmic stability result of [Stefanov, 1990] (up to the value of the exponent).

We consider the inverse scattering problem on the energy interval in three dimensions. We are focused on stability and instability questions for this problem. In particular, we prove an exponential instability estimate which shows optimality of the logarithmic stability result of [Stefanov, 1990] (up to the value of the exponent). 1. Introdution We consider the Schrödinger equation −∆ψ + v(x)ψ ...

In this paper a class of singularly perturbed system of conservation laws is considered. The partial differential equations are equipped with boundary conditions which may be studied to derive the exponential stability. Lyapunov stability technique is used to derive sufficient conditions for the exponential stability of this system. A Lyapunov function in H-norm for a singularly perturbed syste...

Several notions of exponential stability of linear time-invariant systems on arbitrary time scales are discussed. We establish a necessary and sufficient condition for the existence of uniform exponential stability. Moreover, we characterize the uniform exponential stability of a system by the spectrum of its matrix. In general, exponential stability of a system can not be characterized by the ...

the main purpose of this paper is to establish some new results onthe superstability and stability via a fixed point approach forthe pexiderized exponential equation, i.e.,$$|f(x+y)-g(x)h(y)|leq psi(x,y),$$where $f$, $g$ and $h$ are three functions from an arbitrarycommutative semigroup $s$ to an arbitrary unitary complex banachalgebra and also $psi: s^{2}rightarrow [0,infty)$ is afunction. fur...

In this paper we show that uniformly global asymptotic stability for a family of ordinary diierential equations is equivalent to uniformly global exponential stability under a suitable nonlinear change of variables. The same is shown for input-to-state stability and input-to-state exponential stability, and for input-to-state exponential stability and a nonlinear H 1 estimate.