Construction of the Lyapunov function for a class of H∞ norm problem

This paper focuses on how to directly get the accurate solution for the system H
_∞
norm problem. A Lyapunov function construction method is presented. The presented method constructs the Lyapunov function according to the structure parameters of the second-order system, and gives the analytical expression for the H
_∞
norm. Different from the conventional linear matrix inequality (LMI) approaches which need the complex optimization process to get the H
_∞
norm, the presented method gives the analytical expression for the H
_∞
norm. Thus, this paper provides an alternative way to directly get the H
_∞
norm by properly constructing the Lyapunov function. The effectiveness of the presented method is verified by some examples.