Two novel general summation inequalities to discrete-time systems with time-varying delay

This paper presents two novel general summation inequalities, respectively, in the upper and lower discrete regions. Thanks to the orthogonal polynomials defined in different inner spaces, various concrete single/multiple summation inequalities are obtained from the two general summation inequalities, which include almost all of the existing summation inequalities, e.g., the Jensen, the Wirtinger-based and the auxiliary function-based summation inequalities. Based on the new summation inequalities, a less conservative stability condition is derived for discrete-time systems with time-varying delay. Numerical examples are given to show the effectiveness of the proposed approach.