In this paper, we shall present sufficient conditions for the ψ-exponential stability of a class of nonlinear impulsive differential equations. We use the Lyapunov method with functions that are not necessarily differentiable. In the last section, we give some examples to support our theoretical results. Keywords—Exponential stability, globally exponential stability, impulsive differential equa...

This work discusses the asymptotic behavior of a transmission problem on star-shaped networks of interconnected elastic and thermoelastic rods. Elastic rods are undamped, of conservative nature, while the thermoelastic ones are damped by thermal effects. We analyze the overall decay rate depending of the number of purely elastic components entering on the system and the irrationality properties...

In this work we consider a size-structured cannibalism model with the model ingredients (fertility, growth, and mortality rate) depending on size (ranging over an infinite domain) and on a general function of the standing population (environmental feedback). Our focus is on the asymptotic behavior of the system, in particular on the effect of cannibalism on the long-term dynamics. To this end, ...

This work studies certain perturbed and un-perturbed nonlinear systems of continuous discrete integro-delay differential equations (IDDEs). Using the Lyapunov–Krasovskii functional (LKF) method Lyapunov–Razumikhin (LRM), uniform asymptotic stability (UAS), (US), integrability boundedness solutions as well exponential (ES) instability are discussed. In this paper, five new theorems a corollary g...

This paper deals with the simultaneous estimation of attitude, position and linear velocity for vision-aided inertial navigation systems. We propose a nonlinear observer on $SO(3)\times \mathbb{R}^{15}$ relying body-frame acceleration, angular (stereo or monocular) bearing measurements some landmarks that are constant known in frame. Unlike existing local Kalman-type observers, our proposed gua...

A generic parameterization of Lyapunov function candidates is suggested for a quite general class of non-autonomous smooth nonlinear systems. It is shown that conditions for the existence of a Lyapunov function that guarantees uniform exponential stability can be formulated as a set of linear matrix inequalities. Hence, computation of the Lyapunov function involves the solution of a convex opti...

We show here the uniform stabilization of a coupled system of hyperbolic and parabolic PDE’s which describes a particular fluid/structure interaction system. This system has the wave equation, which is satisfied on the interior of a bounded domain Ω, coupled to a “parabolic–like” beam equation holding on ∂Ω, and wherein the coupling is accomplished through velocity terms on the boundary. Our re...

In this paper, dynamic behavior of a class of high-order fuzzy cellular neural networks (HFCNNs) with time-varying delays is investigated. Compared with the previous results in the literature, the restrictions are loosed, since we do not assume the boundedness and monotonicity on the activation functions, and the differentiability of time-varying delay functions. Some sufficient conditions are ...

In this correspondence, we show that the spectrum-determined growth condition holds for the closed-loop system of a vibration cable with a tip mass and linear boundary feedback control. The optimal decay rate of the energy for a case left unsolved in the [1] is determined, and the asymptotic expansion of the associated semigroup is obtained. As a consequence of the approach, we show, in a diffe...