Abstract
This paper investigates the stability of discrete-time Lur'e systems with a time-varying delay. Firstly, an extended-matrix-separated-based summation inequality is established to estimate the summation term containing the system state and the forward difference of the state. Then, an improved delay-product-type Lyapunov-Krasovskii functional (LKF) is proposed, which involves the characteristics of matrices refined and the information of delay squared. By using a quadratic function negative transformation lemma based on matrix-injection, a delay-dependent stability criterion is obtained. Finally, a numerical example demonstrates the advantages of the proposed criterion.
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