Exponential stability of discrete‐time delayed neural networks with saturated impulsive control

Abstract

This paper examines the problem of the locally exponentially stability for impulsive discrete-time delayed neural networks (IDDNNs) with actuator saturation. By fully considering the delay information of the state of the considered system, a new delay-dependent polytopic representation within a discrete-time framework is obtained. Based on the delayindependent polytopic representation approach, the saturation term is expressed as a delaydependent convex combination. In order to obtain some less conservative stability conditions and estimate a larger of the domain of attraction, a novel type of Lyapunov-Krasovskii function (LKF) dependent on the delay information and the impulses instant is proposed, which is called time-dependent LKF. Then, by combining with the proposed LKF, a discrete Wirtinger-based inequality, an extended reciprocally convex matrix inequality and some novel analysis techniques, several new exponential stability criteria dependent on the bounds of the delay are presented. Moreover, when saturation constraints are not considered in the impulsive controller, the stability of the system is also discussed. Finally, two examples are given to confirm the applicability of the proposed results. INTRODUCTIONNeural networks (NNs) have gained considerable research attention in the last few decades because of its wide application in many disciplines including associative memories, pattern recognition, optimization algorithms, and other scientific [1][2][3][4][5][6][7][8]. In addition to this, time delay is inevitable in practical network communication owing to the limited speed of the processor/amplifier [11]. Common types of time delays mainly include discrete delays, distributed delays and neutral delays, and they are generally regarded as main factors causing leading even to its instability. Consequently, it is more meaning to consider delayed NNs. Currently, the research on the dynamics of time-delayed neural networks has received extensive attention, some selected works on NNs with delays are [12][13][14][15][16][17]. Note that the aforementioned NNs are continuous-time dynamical system described by non-linear functional differential equations. However, whenThis is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

Asymptotic stability of non‐instantaneous impulsive systems and T‐S fuzzy non‐instantaneous impulsive control for nonlinear systems

“…For the impulsive control problems, the main advantage is that it is easy to implement with low cost because you only need to control at some discrete points in time. Therefore, impulsive control has been a hot research topic with wide practical application value, see [20][21][22][23][24][25][26][27][28]. Besides, there are series of recent results that allow for the co-existence of both stabilizing and destabilizing jumps simultaneously which undoubtedly reduces the conservatism of control [29][30][31][32][33].…”