Analysis of homogeneous systems with distributed delay using averaging approach

Abstract

The conditions for stability of the zero solution are formulated for homogeneous dynamical systems of non-zero degree with distributed delays. It is assumed that if the disturbances are absent and the non-delayed state substitutes the delayed one, then the obtained nominal system is globally asymptotically stable. In such a case it is proven that in the disturbance-free scenario the zero solution is locally asymptotically stable for positive degree and practically globally asymptotically stable for negative degree. Using averaging tools, the influence of time-varying disturbances is investigated and the respective stability margins are derived. Finally, the obtained theoretical findings are illustrated by a mechanical example.