This article deals with the stability of neural networks (NNs) with time-varying delay. First, a generalized reciprocally convex inequality (RCI) is presented, providing a tight bound for reciprocally convex combinations. This inequality includes some existing ones as special case. Second, in order to cater for the use of the generalized RCI, a novel Lyapunov-Krasovskii functional (LKF) is constructed, which includes a generalized delay-product term. Third, based on the generalized RCI and the novel LKF, several stability criteria for the delayed NNs under study are put forward. Finally, two numerical examples are given to illustrate the effectiveness and advantages of the proposed stability criteria.

This article concerns the stability issues of neural networks with time-varying delays. The purpose is to establish less conservative stability conditions for delayed neural networks. In order to achieve this goal, a time-varying Lyapunov functional method is proposed for stability analysis of delayed neural networks. The main feature of this method is to construct different Lyapunov functionals in different time-varying delay subintervals, which relaxes the restriction requirement of traditional Lyapunov functionals constructing a common Lyapunov functional in the whole delay interval. Based on the developed time-varying Lyapunov functional, some new stability conditions for delayed neural networks are obtained. Finally, two examples are given to verify the effectiveness of the derived stability conditions.

This article studies the stability problems of linear systems with time‐varying delay. An improved negativity condition for a quadratic function parameterised by time‐varying delay is derived. Based on this condition, less conservative stability criteria are obtained. Through two well‐known numerical examples, it is proved that the proposed method can reduce the conservativeness of the computed results.

This paper studies the problem of robust H_∞ active fault-tolerant tracking control for multi-agent systems (MASs) under nonideal communication links and external disturbances. Unlike most existing studies that assume idealized or simplified communication links, such as uniform constant or time-varying delays, this paper considers a more realistic communication scenario involving non-uniform time-varying communication delays. The communication cases discussed encompass existing common communication scenarios as special cases. To achieve active fault-tolerant control, an intermediate variable-assisted proportional-integral observer (PIO) is introduced to estimate the system’s state and faults. Based on fault estimation values and considering non-ideal communication constraints, a fault-tolerant control scheme is designed to achieve the leader-follower tracking control objectives. With the help of Lyapunov theory and matrix inequality method, sufficient criteria are proposed for co-designing the observer and controller gains. Finally, two simulation examples verify the effectiveness of the theoretical results.

This paper investigates the event-triggered (ET) fault-tolerant control problem of T-S fuzzy multi-agent systems (MASs) subject to actuator faults. A novel dynamic event-triggering mechanism is proposed to optimize communication transmission efficiency between agents. This mechanism includes some existing event-triggering mechanisms as exceptional cases and allows flexible adjustment of threshold parameters based on the system state variations. Under this triggering mechanism, the fault-tolerant control problem of MASs is transformed into a stability problem of time-delay systems with the help of artificial time-delay methods. Based on this, an artificial-delay-based looped functional is proposed to improve the existing Lyapunov functional. Then, a sufficient condition for fault-tolerance consensus of MASs, which can tolerate larger ET threshold parameters, is derived. Finally, the effectiveness of the proposed ET fault-tolerant control strategy is validated through application to the Duffing-Van der Pol oscillators. Note to Practitioners —The motivation of this paper is to optimize communication resources and deal with potential actuator failures in cooperative control of MASs, which are widely used in autonomous vehicles, industrial automation, and the Internet of Things. It is noted that frequent communication between MASs will cause communication congestion and reduce control efficiency, and actuator failure will inevitably occur due to physical damage or aging. Thus, the study of ET fault-tolerant control not only helps to optimize communication resources, but also ensures the reliable operation of MASs in the face of actuator abnormal situations, guaranteeing stability and reliability in practical applications. This paper proposes a novel dynamic ET fault-tolerant control protocol to achieve cooperative control objectives in the presence of actuator faults. Additionally, an artificial-delay-based looped functional is constructed to enhance the design flexibility of the ET mechanism and controller. The ET fault-tolerant control strategy is applied to the Duffing-Van der Pol oscillator model to verify its effectiveness and practicability.

In this work, membership-functions-dependent resilient hybrid-triggered (HT) passivity control is considered for networked fuzzy systems against deception attacks. To mitigate the transmission burden and enhance resilience to attacks, a resilient membership-functions-dependent HT mechanism is proposed that considers the properties of a Takagi–Sugeno fuzzy model. The presented HT strategy incorporates membership functions to generalize the HT threshold and weighting matrices. Then, the membership functions are embedded in quadratic and integral terms of the fuzzy Lyapunov–Krasovskii functional, leading to a more effective resilient HT mechanism that significantly reduces network bandwidth stresses and achieves better passivity performance. An asynchronous passivity fuzzy controller with enhanced feasibility is designed under imperfect premise matching, and traditional passive controllers are generalized as special cases. Finally, a truck–trailer example is offered to test the validity and applicability of the proposed techniques.