Discrete free-matrix-based integral inequality and its application

This paper is concerned with the stability problems for discrete linear systems with time-varying delays. A new summation inequality is presented in this paper, which is less conservative than other existing summation inequalities. This inequality is a discrete-time counterpart of the free-matrix-based (FMB) integral inequality. Using it to investigate the stability problem for discrete-time systems, some novel stability criteria are established. The advantage of the derived condition is illustrated by some numerical examples, while a practical example demonstrates the applicability of the method.