Stability of equilibrium positions of mechanical systems with switched force fields

Mechanical system with switched dissipative and potential forces is considered. It is assumed that dissipative forces are linear, whereas potential forces are nonlinear and homogeneous. The conditions of the existence of a common Lyapunov function for corresponding family of subsystems are investigated. The fulfillment of these conditions provides asymptotic stability of the equilibrium position of the switched system for any admissible switching law.