in this paper, global uniform exponential stability of perturbed dynamical systemsis studied by using lyapunov techniques. the system presents a perturbation term which isbounded by an integrable function with the assumption that the nominal system is globallyuniformly exponentially stable. some examples in dimensional two are given to illustrate theapplicability of the main results.

In this paper it is shown that if μ is an n-dimensional Ahlfors-David regular measure in R which satisfies the so-called weak constant density condition, then μ is uniformly rectifiable. This had already been proved by David and Semmes in the cases n = 1, 2 and d − 1, and it was an open problem for other values of n. The proof of this result relies on the study of the n-uniform measures in R. I...

in this paper, we propose a parametric uniform approximation method to solve np-hard absolute value equations. for this, we uniformly approximate absolute value in such a way that the nonsmooth absolute value equation can be formulated as a smooth nonlinear equation. by solving the parametric smooth nonlinear equation using newton method, for a decreasing sequence of parameters, we can get the ...