LMI-Based Results on Robust Exponential Passivity of Uncertain Neutral-Type Neural Networks with Mixed Interval Time-Varying Delays via the Reciprocally Convex Combination Technique

Nayika Samorn,Narongsak Yotha,Kanit Mukdasai,Pantiwa Srisilp

doi:10.3390/computation9060070

Abstract

The issue of the robust exponential passivity analysis for uncertain neutral-type neural networks with mixed interval time-varying delays is discussed in this work. For our purpose, the lower bounds of the delays are allowed to be either positive or zero adopting the combination of the model transformation, various inequalities, the reciprocally convex combination, and suitable Lyapunov–Krasovskii functional. A new robust exponential passivity criterion is received and formulated in the form of linear matrix inequalities (LMIs). Moreover, a new exponential passivity criterion is also examined for systems without uncertainty. Four numerical examples indicate our potential results exceed the previous results.

Highlights

Delayed dynamical systems have been proposed rather extensively because they can be exploited as models to illustrate the transportation systems, communication networks, teleportation systems, physical systems, and biological systems
We consider the nominal system, suggest our main system, in which new criteria of systems are introduced via linear matrix inequalities (LMIs) approach
We considered the robust exponential passivity analysis for uncertain NTNNs with mixed interval time-varying delays including discrete, neutral, and distributed delays

Summary

Introduction

Delayed dynamical systems have been proposed rather extensively because they can be exploited as models to illustrate the transportation systems, communication networks, teleportation systems, physical systems, and biological systems. It is more natural to consider neural networks with activation functions of past state derivative networks Neural networks of this model are called neutral-type neural networks (NTNNs), which have appeared to be useful systems in a variety of applications, including population ecology, propagation, diffusion models and so on. The passivity theory is considered and has played an important role in the astonishing stability of time-delay systems [27,28] It generally has its practical use in signal processing [29], complexity [30], chaos and synchronization control [31], and fuzzy control [32]. As far as we can tell, the robust exponential passivity of the uncertain neutral-type neural networks with mixed interval time-varying delays has never been presented.

Main Results

Numerical Examples

Conclusions