Stability analysis for discrete time-delay systems based on new finite-sum inequalities

A new finite-sum inequality is derived that includes the discrete Jensen's inequality and the Abel lemma-based finite-sum inequality as special cases. Another new inequality, which needs fewer decision variables than the first one and provides a tighter lower bound than the Abel lemma-based finite-sum inequality, is also given. Applying these new inequalities yields new results on stability analysis for discrete time-delay systems. Two numerical examples demonstrate the effectiveness and superiority of the proposed methods.