This note examines stability properties of systems that result from switching among globally asymptotically stable nonlinear systems in triangular form. We show by means of a counterexample that, unlike in the linear case, such a switched system might not be globally asymptotically stable, uniformly over all switching signals. We then formulate conditions that guarantee this uniform global asym...

In this paper, we prove the strong uniform consistency and asymptotic normality of the kernel density estimator proposed by Jones [12] for length-biased data.The approach is based on the invariance principle for the empirical processes proved by Horváth [10]. All simulations are drawn for different cases to demonstrate both, consistency and asymptotic normality and the method is illustrated by ...

Continuous homogeneous controllers are utilized in a full state feedback setting for the uniform finite time stabilization of a perturbed double integrator in the presence of uniformly decaying piecewise continuous disturbances. Semiglobal strong C1 Lyapunov functions are identified to establish uniform asymptotic stability of the closed-loop planar system. Uniform finite time stability is then...

In this work, we prove the existence of a center manifold for some partial functional differential equations, whose linear part is not necessarily densely defined but satisfies the Hille-Yosida condition. The attractiveness of the center manifold is also shown when the unstable space is reduced to zero. We prove that the flow on the center manifold is completely determined by an ordinary differ...

We study certain sufficient conditions for the local and global uniform asymptotic stability, as well as the stabilizability of the equilibrium in cascade systems of delay differential equations. As distinct from the known results, the assertions presented in this paper are also valid for the cases, when the right-hand sides of equations are nonlinear and depend on time or arbitrarily depend on...

We establish, as far as we know, the first proof of uniform global asymptotic stability for a mechanical system (Euler-Lagrange) in closed loop with a dynamic controller which makes use only of position measurements. The controller is fairly simple, it is reminiscent of the so-called PadenPanja controller [20] where unavailable generalized velocities are replaced by approximate differentiation ...

The Lotka-Volterra competition model with diffusion and time delays has been the object of analysis by numerous authors under different approaches. For the case of two species, Ruan and Zhao 1 considered uniform persistence and global extinction; Lu 2 studied global attractivity, and Gourley and Ruan 3 analyzed stability and traveling fronts. The periodic case has also been considered, Feng and...