Improved slack-matrix-based summation inequality and applications to discrete-time systems with time-varying delays

This paper proposes a new slack-matrix-based summation inequality which extends a discrete-time counterpart of a free-matrix-based integral inequality. For a single summation quadratic function, it provides a upper bound which depends on not only the concerned summation interval but also other summation interval. Thus, the proposed summation inequality has more flexibility, which leads to improved stability criteria for discrete-time systems with interval-time-varying delays.