Asymptotic stability conditions for a class of hybrid mechanical systems with switched nonlinear positional forces

Abstract

Stability of the trivial equilibrium position for a class of hybrid mechanical systems with nonswitched linear velocity forces and switched nonlinear nonhomogeneous positional forces is studied. Sufficient conditions in terms of linear matrix inequalities are obtained to guarantee the existence of a common Lyapunov function for the family of subsystems corresponding to a switched system, and therefore to ensure that the equilibrium position of the switched system is asymptotically stable for an arbitrary switching signal. In the case when we are failed to prove the existence of a common Lyapunov function, classes of switching signals are determined for which one can guarantee the asymptotic stability. An example is presented to demonstrate the effectiveness of the proposed approaches.