Stability analysis of systems with time‐varying delay via a delay‐product‐type integral inequality

Abstract

This paper is concerned with the issue of stability analysis of systems with time‐varying delay. First, a delay‐product‐type (DPT) integral inequality is proposed, which combines the third‐order Bessel–Legendre (TOBL) integral inequality and the reciprocally convex (RC) inequality into a unified integral inequality; then, a tight upper bound on the time‐derivative of the Lyapunov–Krasovskii functional (LKF) can be obtained. Second, an augmented LKF is tailored for the use of the DPT integral inequality; then, more information about the instant state and the delayed states is taken into account. Third, by using the DPT integral inequality and the augmented LKF, some less conservative conditions that ensure the stability of systems with time‐varying delay are derived. Finally, simulations are provided to illustrate the advantage of our proposed method.

Consensus of multi-agent systems with state-dependent intermittent communication

“…Coordinated control of multi-agent systems has received great concerns in the last decade because of their wide applications in spacecraft formation, robot manipulators, biological systems, and so forth (Sun et al, 2022a, 2022b, 2022c, 2022d; Tan and Wang, 2022; Yan et al, 2018). Consensus is a significant behavior of multi-agent systems, in which the states of all the agents aim at reaching the same trajectory (Sun et al, 2020a).…”

General stability criteria for time‐delay systems using a new delay‐dependent reciprocally convex inequality

“…Moreover, the authors in Yang et al [28] have utilized a convex analysis method to employ several conditions for achieving fixed‐time synchronization of NNs with time‐varying delays. In addition, few studies developed the RCI into generalized $$$ m $$$‐ degree polynomial format to estimate the derivative of the LKFs [29–32]. One such advancement has presented in Chen et al [29], which introduced a high‐order matrix polynomial with an undetermined parameter $$$ m $$$ to develop an RCI containing the original one.…”

“…In Lin et al [30], a generalized RCI has been established by using an $$$ m $$$‐degree matrix‐valued polynomial to investigate delayed NNs. Further, a delay‐product type integral inequality has been formulated to address the LKF derivative by combining the third‐order Bessel–Legendre integral inequality and the RCI [31].…”

Harmonic and synchronous compound control of a dual-valve controlled single-rod electro-hydraulic actuator

“…If the multiple valves work synchronously, it is usually called synchronous control. 7–9 If they work sequentially, it is called harmonic or asynchronous control. 10 Fang et al 11 adopted a synchronous control scheme with multiple servo valves to ensure the tracking accuracy of the hydraulic system under large flow by eliminating the synchronization error of the valves.…”