Auxiliary function-based integral inequalities for quadratic functions and their applications to time-delay systems

Finding integral inequalities for quadratic functions plays a key role in the field of stability analysis. In such circumstances, the Jensen inequality has become a powerful mathematical tool for stability analysis of time-delay systems. This paper suggests a new class of integral inequalities for quadratic functions via intermediate terms called auxiliary functions, which produce more tighter bounds than what the Jensen inequality produces. To show the strength of the new inequalities, their applications to stability analysis for time-delay systems are given with numerical examples.