Dual approach to Lyapunov stability

We investigate the problem of Lyapunov stability for nonautonomous ODEs for which the right-hand side is only Lebesgue-measurable with respect to time tt, x′=f(t,x)x′=f(t,x). We describe how to use the dual Lyapunov function in dual space and the Hamilton–Jacobi inequality to formulate sufficient conditions for the stability of the zero solution in primary and dual space.