New Stability Criteria of Discrete Systems With Time-Varying Delays

Abstract

This paper is concerned with the stability criteria of discrete neural networks with two additive input time-varying delays. By using the time delay division and a new summation inequality, a less conservative criterion is derived. Moreover, to compare the obtained criterion more directly with the existing results, a corollary is proposed accordingly. Finally, some numerical examples are presented to demonstrate that the obtained criteria are less conservative. INDEX TERMS Discrete neural networks, Lyapunov-Krasovskii functionals, stability, time-varying delays.

Enhanced Stability Criteria for Discrete-time Systems with Time-varying Delay

“…Recently, we note that the robust stability problem of discrete-time systems with interval time-varying delays has become a great theoretical topic [23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38]. Among these works, lots of LMI-based stability criteria have been presented via the LKF approach.…”

“…The delay decomposition approach is used in [28,32], where delay decomposition interval-dependent stability criteria are derived via LKF approach. In terms of focusing on estimating the upper bound of the difference of the LKF, a lot of tight inequality techniques can be found in [25, 29-31, 33, 35-39], such as, estimating the upper bound on the difference of the LKF via the free-weighting matrix approach without ignoring some important terms [25], new discrete inequalities for single summation and double summation [30,40], discrete Wirtinger-based inequality approach [35,36], etc. It is worth emphasizing that Nthorder discrete Legendre polynomials-based inequality and Bessel summation inequality are proposed in [38,41], respectively, where N-dependent stability criteria are given.…”

“…It is worth emphasizing that Nthorder discrete Legendre polynomials-based inequality and Bessel summation inequality are proposed in [38,41], respectively, where N-dependent stability criteria are given. The results of [38,41] show that the conservativeness de-creases with the increase of N. Two general free-matrixbased summation inequalities are proposed in [36,42] based on second-order Bessel summation inequality, respectively. However, the upper bounds of the summations with respect to the time delay intervals [h 1 , h(k)] and [h(k), h 2 ] are always estimated separately based on the Legendre polynomials-based inequality, Bessel summation inequality above or the general free-matrix-based summation inequality.…”

New Results on Stability of Linear Discrete-Time Systems With Time-Varying Delay

“…On the other hand, a proper introduction of small delay can make an unstable system become stable or improve dynamic performances [1]. Therefore, during past decades, linear discrete-time systems with a timevarying delay have attracted extensive attention from academic research [4]- [12] and a number of remarkable results have been reported in the literature [13]- [24].…”

An Insight into Stability Conditions of Discrete-Time Systems With Time-Varying Delay

“…Since time delay is often encountered in the real world such as network and mechanical engineering [1], [2], the stability analysis for discrete-time systems with time-varying delay has attracted considerable attention. Until now, many remarkable results have been reported in the literature [1]- [39] such as the free-matrix-weighting technique [3], the delaypartitioning method [4], the bounding-equality method [1], [5]- [7]. Compared with other techniques, the boundinginequality method, owing to its effectiveness and straightforwardness, has been widely used in the Lyapunov-Krasovskii (L-K) functional method.…”