The Discussion Of The Problems Of The Finite-time Stability

In this paper,the finite-time stability of linear systems is discussed. First of all,the problem of the finite-time stability of a discrete system is studied and three relative theorems are given based on LMI. Then linear time-delay system is discussed and a sufficient and necessary condition is given based on LMI also. At last, combined the finite-time stability with traditional H~∞control problem, a sufficient condition which solves the finite-time H~∞control problem of a class of continuous systems is obtained.