Second-order Approximation Integral Inequality for Stability of Systems with Time Delays

This paper proposed a new integral inequality, called second-order approximation integral inequality (SAII), that could significantly reduce the conservativeness in stability analysis of systems with time delays. The former well-known integral inequalities such as Jensen's inequality and Wirtinger based inequality, are all included in the proposed integral inequality as special cases. Furthermore, it's shown that Jensen's and Wirtinger based inequalities are just zero-order and first-order approximation, respectively. Stability criterion with less conservatism is then developed using SAII for time delay systems. Numerical examples are given to demonstrate the effectiveness and benefit of the proposed method.