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Global asymptotic stability is an important issue for wide applications of recurrent neural networks with time-varying delays. The Lyapunov–Krasovskii functional method is a powerful tool to check the global asymptotic stability of a delayed recurrent neural network. When the Lyapunov–Krasovskii functional method is employed, three steps are necessary in order to derive a global asymptotic stability criterion: (i) constructing a Lyapunov–Krasovskii functional, (ii) estimating the derivative of the Lyapunov–Krasovskii functional, and (iii) formulating a global asymptotic stability criterion. This paper provides an overview of recent developments in each step with insightful understanding. In the first step, some existing Lyapunov–Krasovskii functionals for stability of delayed recurrent neural networks are anatomized. In the second step, a free-weighting matrix approach, an integral inequality approach and its recent developments, reciprocally convex inequalities and S -procedure are analyzed in detail. In the third step, linear convex and quadratic convex approaches, together with the refinement of allowable delay sets are reviewed. Finally, some challenging issues are presented to guide the future research. [ABSTRACT FROM AUTHOR]

This paper is concerned with event-triggered H ∞ control for a class of nonlinear networked control systems. An event-triggered transmission scheme is introduced to select 'necessary' sampled data packets to be transmitted so that precious communication resources can be saved significantly. Under the event-triggered transmission scheme, the closed-loop system is modeled as a system with an interval time-varying delay. Two novel integral inequalities are established to provide a tight estimation on the derivative of the Lyapunov-Krasovskii functional. As a result, a novel sufficient condition on the existence of desired event-triggered H ∞ controllers is derived in terms of solutions to a set of linear matrix inequalities. No parameters need to be tuned when controllers are designed. The proposed method is then applied to the robust stabilization of a class of nonlinear networked control systems, and some linear matrix inequality-based conditions are formulated to design both event-triggered and time-triggered H ∞ controllers. Finally, two numerical examples are given to demonstrate the effectiveness of the proposed method. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY This paper studies the stability of linear systems with interval time-varying delays. By constructing a new Lyapunov-Krasovskii functional, two delay-derivative-dependent stability criteria are formulated by incorporating with two different bounding techniques to estimate some integral terms appearing in the derivative of the Lyapunov-Krasovskii functional. The first stability criterion is derived by using a generalized integral inequality, and the second stability criterion is obtained by employing a reciprocally convex approach. When applying these two stability criteria to check the stability of a linear system with an interval time-varying delay, it is shown through some numerical examples that the first stability criterion can provide a larger upper bound of the time-varying delay than the second stability criterion. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]