On design of time optimal systems via the second method of Lyapunov

Two theorems with applications are presented in this paper. It is shown that a particular application of the second method of Lyapunov yields the time optimal solution to the feedback design problem for a class of systems satisfying conditions of Theorem 1. Theorem 2 can be used to design a class of feedback systems satisfying any given settling time in terms of initial perturbations of the plant.