In this work characterizations of the notion of non-uniform in time robust global asymptotic output stability for hybrid systems with disturbances are given. Based on the provided characterizations, it is shown that every asymptotically output controllable time-varying control system can be stabilized (in general nonuniformly in time) by means of time-varying hybrid feedback.

AMract-We present a methodology based on the energy shaping framework to derive strict Lyapunov functions for a class of global regulators for robot manipulators. The class of controllers is described by control laws composed by the gradient of an artificial potential energy plus a linear velocity feedback. We provide explicit sufficient conditions on the artificial potential energy that allow ...

A class of nonlinear nonstationary systems of Persidskii type is studied. The right-hand sides of the systems are represented in the form of linear combinations of sector nonlinearities with time-varying coefficients. It is assumed that the coefficients possess mean values. By means of the Lyapunov direct method, it is proved that if the investigated systems are essentially nonlinear, i.e. the ...

This paper introduces incremental stability notions for a class of hybrid dynamical systems given in terms of differential equations and difference equations with state constraints. The specific class of hybrid systems considered are those that do not have consecutive jumps nor Zeno behavior. The notion of incremental asymptotic stability is used to describe the behavior of the distance between...

‎this paper deals with the singular sturm-liouville expressions‎ ‎$ ‎ell y =‎ -‎y''+q(x)y=lambda y‎ ‎$‎ ‎on a finite interval‎, ‎where the potential function $q$ is real and‎ ‎has a singularity inside the interval‎. ‎using the asymptotic estimates of a‎ ‎spectral fundamental system of solutions of sturm-liouville‎ ‎equation‎, ‎the asymptotic form of the solution of the‎ ‎equation (0.1) and the ...

Consideration of manipulator dynamics and external disturbances in robot control system design can enhance the stability and performance properties of the whole system. In this paper, we present an approach to solve the control problem when the inertia parameters of robot are unknown, and at the same time robot is subjected to external force disturbances. This approach is based on simultaneous ...

We study nonlinear time-asymptotic stability of small–amplitude planar Lax shocks in a model consisting of a system of multi–dimensional conservation laws coupled with an elliptic system. Such a model can be found in context of dynamics of a gas in presence of radiation. Our main result asserts that the standard uniform Evans stability condition implies nonlinear stability. The main analysis is...

We study nonlinear asymptotic stability of small–amplitude Lax shocks in a model consisting of a system of multi–dimensional conservation laws coupled with an elliptic system. Such a model can be found in context of dynamics of a gas in presence of radiation. Our main result asserts that the standard uniform Evans stability condition implies nonlinear stability. The main analysis is based on th...