Stability of Stationary Sets in Nonlinear Systems with Set-valued Friction

Abstract

In this paper we present conditions under which an equilibrium set of a multi-degree-of-freedom nonlinear mechanical system, with set-valued friction and an arbitrary number of frictional bilateral constraints, is attractive. These systems form an important class of hybrid engineering systems. The attractivity results are obtained using the framework of differential inclusions together with a Lyapunov-type stability analysis and LaSalle's invariance principle. The special structure of mechanical systems allows for a natural Lyapunov function candidate and a generic result for a large class of systems. Moreover, an instability theorem for assessing the instability of equilibrium sets of differential inclusions is presented. These results are illustrated by means of an example of a nonlinear mechanical system exhibiting both attractive and unstable equilibrium sets.