Stability and Stabilization of Mechanical Systems with Switching

Hybrid mechanical systems with switched force fields, whose motions are described by differential second-order equations are considered. We propose two approaches to solving problems of analysis of stability and stabilization of an equilibrium position of the named systems. The first approach is based on the decomposition of an original system of differential equations into two systems of the same dimension but of the first order. The second approach is in direct specifying a construction of a general Lyapunov function for a mechanical system with switching.