New augmented Lyapunov–Krasovskii functional approach to stability analysis of neural networks with time-varying delays

New delay-interval-dependent stability analysis of neutral type BAM neural networks with successive time delay components

“…to LKF in [38]. In this paper robust stability analysis for neutral type BAM networks with additive time-varying delays is developed by constructing a new LKF with four integral terms such as d 3…”

Exponential Synchronization of Neural Networks via Feedback Control in Complex Environment

“…In hardware implementation, time delays are inevitable due to the inherent information delivery time between neurons and the finite switching speed of amplifiers. The existence of time delays usually causes oscillation, divergence, or even instability of a system [5,6], thus a large number of scholars have conducted a number of studies in regard to the dynamic behavior of the delayed neural networks [7][8][9]. From the perspective of time delays, all the research results can be divided into time-dependent and time-independent.…”

New generalized Halanay inequalities with applications to stability of nonlinear non-autonomous time-delay systems

“…A popular approach in stability analysis for timedelay systems is the use of the Lyapunov-Krasovskii functional method [7,[14][15][16] and its variants, such as the Razumikhin-type theorem [17,18], to derive sufficient conditions in terms of linear matrix inequalities (LMIs) or matrix Riccati differential equations (RDEs). These conditions can be classified into two types, namely delay-dependent conditions and delayindependent conditions.…”

“…Therefore, more attention has been devoted to derive less conservative delay-dependent stability conditions for time-delay systems with the key objective in achieving a maximum allowable delay bound (MADB). This task relies heavily on how to choose an appropriate Lyapunov-Krasovskii functional candidate and how to utilize some improved inequalities (such as the Cauchy-Schwartz, Jensen, reciprocally convex combination and Wirtinger inequality) combining with some effective techniques (such as model transformation, delay decomposition, delay distribution and free-weighting matrix) to derive the least conservative bound on the derivatives of the chosen LyapunovKrasovskii functional candidate [14,16]. In particular, we refer the reader to the most recent paper [19] in which the authors reported a significant improvement on the MADB for time-delay systems with differentiable and bounded time-varying delays.…”