In this paper, we are interested in investigating notions of stability for generalized linear differential equations (GLDEs). Initially, propose and revisit several definitions provide a complete characterisation them terms upper bounds asymptotic behaviour the transition matrix. addition, illustrate our results GLDEs to periodic systems impulsive equations. Finally, prove that well known unifo...

In this paper, we investigate the effect of time delays in boundary or internal feedback stabilization of the multidimensional Schrödinger equation. In both cases, under suitable assumptions, we establish sufficient conditions on the delay term that guarantee the exponential stability of the solution. These results are obtained by using suitable energy functionals and some observability estimates.

Three competing mathematical fitting models (a point-by-point estimation method, a linear fit method, and an isoconversion method) of chemical stability (related substance growth) when using high temperature data to predict room temperature shelf-life were employed in a detailed comparison. In each case, complex degradant formation behavior was analyzed by both exponential and linear forms of t...

We consider the Timoshenko system in a bounded domain (0, L) ⊂ R1. The system has an indefinite damping mechanism, i.e. with a damping function a = a(x) possibly changing sign, present only in the equation for the rotation angle. We shall prove that the system is still exponentially stable under the same conditions as in the positive constant damping case, and provided a = ∫ L 0 a(x) dx > 0 and...

Random exponential marking (REM) is an attractive adaptive queue management algorithm. It uses the quantity known as ‘price’ to measure the congestion in a network. REM can achieve high utilisation, small queue length, and low buffer overflow probability. Many works have used control theory to provide the stable condition of REM without considering the feedback delay. Recently, sufficient condi...

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).

The Yee-method is a simple and elegant way of solving the time-dependent Maxwell’s equations. On the other hand this method has some inherent drawbacks too. The main one is that its stability requires a very strict upper bound for the possible time-steps. This is why, during the last decade, the main goal was to construct such methods that are unconditionally stable. This means that the time-st...