Auxiliary Function-based Summation Inequalities for Quadratic Functions and their Application to Discrete-time Delay Systems∗

Jensen inequality has become a powerful tool of supporting summation inequalities for quadratic functions in order to obtain stability criteria for time-delayed systems since it achieves remarkable performance with a small number of decision variables. This paper suggests a new summation inequality for quadratic functions based on an auxiliary function, which is superior to the Jensen inequality. To demonstrate the superiority of the new inequality, its application to stability analysis for discrete-time delay system is provided with a simple numerical example.