The Method of Limit Equations for Nonautonomous Systems with Delay Using Several Lyapunov Functionals

The method of limit differential equations in combination with the direct method of Lyapunov functions with sign-definite derivatives is an effective tool for studying the asymptotic behavior of solutions of nonautonomous systems. In this paper the method is presented in the form of generalizations of the LaSalle invariance principle for functional differential inclusions with delay using a set of additional Lyapunov functionals. The method is illustrated on a mechanical system with Coulomb friction in the form of Lagrange equations of the second kind.