Invariance Principle for Nonautonomous Functional-Differential Equations with Discontinuous Right-Hand Sides

For nonautonomous functional-differential equations with piecewise continuous right-hand sides and solutions understood in the sense of A.F. Filippov, the method of limit differential inclusions is proposed to study the asymptotic properties of solutions. Properties of the type of the invariance of omega-limit sets and analogues of LaSalle's invariance principle are proved by applying invariantly differentiable Lyapunov functionals with derivatives of constant sign.