Hybrid Feedback Control for Exponential Stability and Robust H∞ Control of a Class of Uncertain Neural Network with Mixed Interval and Distributed Time-Varying Delays

Charuwat Chantawat,Rattaporn Supama,Thongchai Botmart,Sakda Noinang,Wajaree Weera

doi:10.3390/computation9060062

Charuwat Chantawat, Rattaporn Supama + Show 3 more

Open Access

https://doi.org/10.3390/computation9060062

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Abstract

This paper is concerned the problem of robust H∞ control for uncertain neural networks with mixed time-varying delays comprising different interval and distributed time-varying delays via hybrid feedback control. The interval and distributed time-varying delays are not necessary to be differentiable. The main purpose of this research is to estimate robust exponential stability of uncertain neural network with H∞ performance attenuation level γ. The key features of the approach include the introduction of a new Lyapunov–Krasovskii functional (LKF) with triple integral terms, the employment of a tighter bounding technique, some slack matrices and newly introduced convex combination condition in the calculation, improved delay-dependent sufficient conditions for the robust H∞ control with exponential stability of the system are obtained in terms of linear matrix inequalities (LMIs). The results of this paper complement the previously known ones. Finally, a numerical example is presented to show the effectiveness of the proposed methods.

Highlights

It has been shown that the presence of time delay in a dynamical system is often a primary source of instability and performance degradation [15]
Most of works have been focused on the problem of designing a robust H∞ controller that stabilizes linear uncertain systems with time-varying norm bounded parameter uncertainty in the state and input matrices
In this paper we have considered the problem of a robust H∞ control for a class of uncertain systems with interval and distributed time-varying delays

Summary

Introduction

The problem of the reliable control has received much attention [1,2,3,4,5,6,7,8,9,10,11]. Many researchers have paid attentions to the problem of robust stability for uncertain systems with time delays [16,17,18,19]. Most of works have been focused on the problem of designing a robust H∞ controller that stabilizes linear uncertain systems with time-varying norm bounded parameter uncertainty in the state and input matrices. In this paper we have considered the problem of a robust H∞ control for a class of uncertain systems with interval and distributed time-varying delays. This research is the first time to study hybrid feedback control for exponential stability and robust H∞ control of a class of uncertain neural network with mixed interval and distributed time-varying delays.

Model Description and Mathematic Preliminaries

Stability Analysis

Numerical Examples

Conclusions