Finite-Time Passivity-Based Stability Criteria for Delayed Discrete-Time Neural Networks via New Weighted Summation Inequalities

Abstract

In this paper, we study the problem of finite-time stability and passivity criteria for discrete-time neural networks (DNNs) with variable delays. The main objective is how to effectively evaluate the finite-time passivity conditions for NNs. To achieve this, some new weighted summation inequalities are proposed for application to a finite-sum term appearing in the forward difference of a novel Lyapunov-Krasovskii functional, which helps to ensure that the considered delayed DNN is passive. The derived passivity criteria are presented in terms of linear matrix inequalities. A numerical example is given to illustrate the effectiveness of the proposed results.

Finite‐Time Nonfragile Dissipative Control for Discrete‐Time Neural Networks with Markovian Jumps and Mixed Time‐Delays

“…Conventional dissipative theory discussed the asymptotic behavior of the system over an infinite-time interval, while the proposed dissipative methods of this paper provide an input-output energy-related characterization to the analysis in a specified finite-time interval. On the other hand, the dissipative control considered in this paper is more general than most of existing finite-time stabilization, finite-time ∞ control, and FTP control [25][26][27][28][29][30][31], which contains ∞ performance and passive performance as two special cases by choosing appropriate parameters W, S, and R in inequality (10). When setting W = − , S = 0, and R = ( + 2 ) , the performance prescribed in Definition 6 becomes stochastic finite-time ∞ performance [27][28][29][30]; if W = 0, S = , and R = 2 , then it corresponds to FTP performance [31].…”

“…Yang et al dealt with the FTS for singular system [26]. Subsequently, FTS was extended to finite-time boundedness (FTB), the finite-time ∞ control, finite-time passive (FTP) control, and so on [27][28][29][30][31]. And recently, Ma et al studied the finite-time dissipative (FTD) problem of singular discrete-time Markov jump systems [32].…”

“…The main contributions of this paper can be highlighted. (1) A more comprehensive model of discrete-time NNS is proposed that contains Markovian jumps and mixed delays than existing literatures [30,31], since the Markovian jumps and mixed delays were not considered in [30,31]. (2) By applying stochastic analysis method and LMI tool, sufficient conditions for the stochastic finite-time boundedness and stochastic finite-time dissipativity of the discrete-time NNS with Markovian jumps and mixed delays are given.…”

Stability, Finite-Time Stability and Passivity Criteria for Discrete-Time Delayed Neural Networks

“…Delays in a system may cause oscillation and divergence and further degrade the performance [5][6][7][8][9][10]. Since most systems use a digital processor to acquire information from computers at discrete instants of time, it is essential to formulate discrete-time neural networks (DNNs) that are an analogue of continuous ones [11][12][13][14][15][16][17][18]. In order to improve results regarding this problem, various techniques have been applied to the delay-dependent category, such as augmented Lyapunov-Krasovskii (LK) functional [13,[19][20][21][22], free-weighting matrix method [18,23], summation inequality method [16,[24][25][26][27], delay-partitioning method [5,28,29] and reciprocally convex approach [20,30,31].…”

New double integral inequality with application to stability analysis for linear retarded systems

“…From the literature, it is noted that the conservatism of Jensen's inequality can be reduced by using the WBDII as well as FMBDII and will provide a tighter lower bound of the double integral form. In this spirit and the discrete-time case, all the cross-terms of the derivative of the LKF are bounded using discrete inequalities like Jensen's discrete inequalities [38], the discrete WBI was reported in [39,40], discrete inequalities based on multiple auxiliary functions were presented in [41], and a novel summation inequality was proposed in [42,62] to analyse the stability of discrete-time systems. Bessel summation inequalities for the stability analysis of discrete-time systems with time-varying delays were proposed in [43].…”