Asymptotic relationship between trajectories of nominal and uncertain nonlinear systems on time scales

Abstract

This paper studies the relationship between trajectories of nominal and uncertain nonlinear systems evolving on non-uniform time domains. The theory of dynamic equations on time scale is used to analyze the stability of perturbed nonlinear systems. First, it will be shown that the error between the uncertain and the nominal trajectories remains bounded for a particular class of systems. Then, using the Lyapunov theory, some conditions are derived to guarantee that the trajectory of the perturbed system exponentially converges to the trajectory of the corresponding nominal system. These results are useful to study the robustness properties of uncertain nonlinear systems evolving on non-uniform time domains.