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This article investigates the stability analysis of discrete‐time neural networks with time‐varying delays by the utilization of quadratic delay information. First, three extended negative‐definiteness lemmas for matrix‐valued quadratic function with different matrices injection are established. Second, a novel delay‐product‐type Lyapunov functional with the asymmetric summation is developed to relax the positive‐definiteness of functional. Then, the proposed negative definite approaches are utilized in combination with some typical summation inequalities to realize the construction of linear matrix inequalities. Based on these improved technologies, two delay‐dependent stability criteria with less conservatism and fewer computational burdens are derived. Finally, several numerical examples are presented to show the validity and superiority of the proposed methods. [ABSTRACT FROM AUTHOR]

This article is concerned with the stability and stabilization of delayed discrete-time T–S fuzzy systems. The purpose is to develop less conservative stability analysis and state-feedback controller design methods. First, a matrix-separation-based inequality is proposed, which can provide a tighter estimation for the augmented summation term. Then, by constructing a delay-product-type Lyapunov–Krasovskii functional, using the proposed inequality to estimate its forward difference and using a cubic functional negative-determination lemma to handle nonconvex conditions with respect to the delay, a delay and its variation-dependent stability criterion are obtained. Moreover, the corresponding controller design method for closed-loop delayed fuzzy systems is derived via parallel distributed compensation scheme. Finally, two examples are given to demonstrate the effectiveness and merits of the proposed approaches. [ABSTRACT FROM AUTHOR]

This brief concerns the stability of fixed-point state-space digital filters with generalized overflow arithmetic and a time-varying delay. A relaxed lemma that includes a commonly used lemma as a special case is developed to show the relationship between the state and the overflow arithmetic, and a Lyapunov functional with positive-definite conditions that are more relaxed than usual is constructed. As a result, a less conservative stability criterion is established, and the efficiency and merit of the criterion are illustrated with a numerical example. [ABSTRACT FROM AUTHOR]

Conclusion: This study has investigated the stability of discrete-time systems with a time-varying delay. To handle the negativity condition of the forward difference of Lyapunov function, a matrix-injection-based method has been developed to convert the original negativity condition to an equivalent tractable matrix inequality by injecting a few matrices. By using this method and an augmented Lyapunov function, a stability criterion with less conservatism for the delayed linear discrete-time system has been developed. The case study via a numerical example has shown the merit of the criterion. It is predictable that the proposed method, together with the methods recently reported by [9], can further improve the results. [ABSTRACT FROM AUTHOR]