scholarly journals Finite-time Stability, Dissipativity and Passivity Analysis of Discrete-time Neural Networks Time-varying Delays

2019 ◽  
Vol 3 (6) ◽  
pp. 361-368
Author(s):  
Porpattama Hammachukiattikul
Keyword(s):  
Neural Networks ◽  
Discrete Time ◽  
Finite Time ◽  
Linear Matrix ◽  
Time Varying ◽  
Time Stability ◽  
Finite Time Stability ◽  
Time Varying Delay ◽  
The Neural Network ◽  
Network Time

The neural network time-varying delay was described as the dynamic properties of a neural cell, including neural functional and neural delay differential equations. The differential expression explains the derivative term of current and past state. The objective of this paper obtained the neural network time-varying delay. A delay-dependent condition is provided to ensure the considered discrete-time neural networks with time-varying delays to be finite-time stability, dissipativity, and passivity. This paper using a new Lyapunov-Krasovskii functional as well as the free-weighting matrix approach and a linear matrix inequality analysis (LMI) technique constructing to a novel sufficient criterion on finite-time stability, dissipativity, and passivity of the discrete-time neural networks with time-varying delays for improving. We propose sufficient conditions for discrete-time neural networks with time-varying delays. An effective LMI approach derives by base the appropriate type of Lyapunov functional. Finally, we present the effectiveness of novel criteria of finite-time stability, dissipativity, and passivity condition of discrete-time neural networks with time-varying delays in the form of linear matrix inequality (LMI).

scholarly journals H_∞ Finite-time Boundedness for Discrete-time Delay Neural Networks via Reciprocally Convex Approach

2020 ◽  
Vol 36 (3) ◽  
Author(s):  
Le Anh Tuan
Keyword(s):  
Neural Networks ◽  
Discrete Time ◽  
Finite Time ◽  
Linear Matrix ◽  
Time Varying ◽  
Time Stability ◽  
Finite Time Stability ◽  
Discrete Time Delay ◽  
Finite Time Boundedness ◽  
Reciprocally Convex Approach

This paper addresses the problem of finite-time boundedness for discrete-time neural networks with interval-like time-varying delays. First, a delay-dependent finite-time boundedness criterion under the finite-time  performance index for the system is given based on constructing a set of adjusted Lyapunov–Krasovskii functionals and using reciprocally convex approach. Next, a sufficient condition is drawn directly which ensures the finite-time stability of the corresponding nominal system. Finally, numerical examples are provided to illustrate the validity and applicability of the presented conditions. Keywords: Discrete-time neural networks,  performance, finite-time stability, time-varying delay, linear matrix inequality.  

scholarly journals Robust Finite-time Boundedness of Discrete-time Neural Networks with Time-varying Delays

2021 ◽  
Vol 17 ◽  
pp. 146-155
Author(s):  
Mengying Ding ◽  
Yali Dong
Keyword(s):  
Neural Networks ◽  
Discrete Time ◽  
Finite Time ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Finite Time Stability ◽  
Time Varying Delay ◽  
Finite Time Boundedness ◽  
Varying Delay

This paper is concerned with the problem of robust finite-time boundedness for the discrete-time neural networks with time-varying delays. By constructing an appropriate Lyapunov-Krasovskii functional, we propose the sufficient conditions which ensure the robust finite-time boundedness of the discrete-time neural networks with time-varying delay in terms of linear matrix inequalities. Then the sufficient conditions of robust finite-time stability for the discrete-time neural networks with time-varying delays are given. Finally, a numerical example is presented to illustrate the efficiency of proposed methods.

scholarly journals New Results for Finite-Time Stability of Discrete-Time Linear Systems with Interval Time-Varying Delay

2015 ◽  
Vol 2015 ◽  
pp. 1-15 ◽  
Author(s):  
Sreten B. Stojanovic
Keyword(s):  
Discrete Time ◽  
Finite Time ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Time Stability ◽  
Finite Time Stability ◽  
Time Varying Delay ◽  
Maximum Delay ◽  
Varying Delay

The problem of finite-time stability for linear discrete time systems with state time-varying delay is considered in this paper. Two finite sum inequalities for estimating weighted norms of delayed states are proposed in order to obtain less conservative stability criteria. By using Lyapunov-Krasovskii-like functional with power function, two sufficient conditions of finite-time stability are proposed and expressed in the form of linear matrix inequalities (LMIs), which are dependent on the minimum and maximum delay bounds. The numerical example is presented to illustrate the applicability of the developed results. It was shown that the obtained results are less conservative than some existing ones in the literature.

scholarly journals Finite-Time Passivity Analysis of Neutral-Type Neural Networks with Mixed Time-Varying Delays

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3321
Author(s):  
Issaraporn Khonchaiyaphum ◽  
Nayika Samorn ◽  
Thongchai Botmart ◽  
Kanit Mukdasai
Keyword(s):  
Neural Networks ◽  
Integral Inequality ◽  
Finite Time ◽  
Neutral Type ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Time Stability ◽  
Finite Time Stability ◽  
Passivity Analysis

This research study investigates the issue of finite-time passivity analysis of neutral-type neural networks with mixed time-varying delays. The time-varying delays are distributed, discrete and neutral in that the upper bounds for the delays are available. We are investigating the creation of sufficient conditions for finite boundness, finite-time stability and finite-time passivity, which has never been performed before. First, we create a new Lyapunov–Krasovskii functional, Peng–Park’s integral inequality, descriptor model transformation and zero equation use, and then we use Wirtinger’s integral inequality technique. New finite-time stability necessary conditions are constructed in terms of linear matrix inequalities in order to guarantee finite-time stability for the system. Finally, numerical examples are presented to demonstrate the result’s effectiveness. Moreover, our proposed criteria are less conservative than prior studies in terms of larger time-delay bounds.

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