Improved exponential stability of time-delay systems

In this paper, a new inner product space is defined, which has a standard orthogonal basis. Based on this basis, an improved integral inequality is established, which is used to construct a new Lyapunov-Krasovskii functionals (LKFs). Thus, a less conservative exponential stability criterion of time-delay systems is obtained, which is in form of linear matrix inequalities(LMIs). Finally, non-conservatism of this exponential stability criterion can be not only numerically illustrated by an example, but also rigorously proved in theory.