Novel criteria for attractivity and stability of non-autonomous nonlinear dynamical systems

In this paper, issues of both attractivity and stability for some classes of nonlinear systems are investigated. New sufficient conditions for practical h-stability of non-autonomous nonlinear systems depending on a parameter are proposed by indefinite Lyapunov functions. We present new converse Lyapunov theorems for non-autonomous systems. The h-stability analysis is achieved with the help of scalar practical h-stable functions. These results are used to study the uniform practical h-stability of non-autonomous perturbed systems.