Stability of discrete-time delayed systems via convex function-based summation inequality

Summation inequalities method for quadratic functions plays a key role in the field of stability analysis, in which the information of time-varying delay and states can be introduced. Generally, the information of delay variation is introduced by the forward difference of Lyapunov–Krasovskii functional, which may lead to some underutilized delay information due to its internal constraints. This paper proposes a new summation inequality for quadratic functions by defining a set of convex functions, which simultaneously introduces the delay amplitude and variation in a summation inequality. A delay amplitude and variation-dependent stability criterion is obtained by using the summation inequality. A numerical example is given to substantiate the effectiveness of the proposed methods.