3. Homogeneity

As we have seen in the previous section, existence of a proper Lyapunov function is necessary and sufficient for appearance of accelerated convergence in the dynamics. However, it is a well-known fact that it is very difficult to find a suitable Lyapunov function for a nonlinear system, even to establish an asymptotic convergence and stability. Consequently, for the case of accelerated convergence, taking into account the additional strict requirements, the design of a Lyapunov function becomes much more difficult (see