Attainability set of a mechanical controlable system and conditions of robust stability

Abstract

In this work, the boundary of the attainabbility set of a second order differential equation with an external perturbation is determined numerically, using the solution of the problem of the maximum variation of the oscillation amplitudes of its solutions. The method consists in determining, in a given set of functions, the external perturbation that causes maximum oscillation amplitudes in the solutions of the dierential equation that describes, as a particular case, the dynamics of a controllable mechanical system with impacts. With the help of this perturbation, the existence of a closed path that describes the boundary of the reachability set is determined, which allow to establish suffcient conditions on the robust stability of the solutions of the differential equation. The results are illustrated numerically in particular cases.

Keywords

• ecuaciones diferenciales
• sistemas de control no lineal
• perturbaciones
• estabilidad