Improved Results on Delay-Dependent Robust    H   ∞    Control of Uncertain Neutral Systems with Mixed Time-Varying Delays

Jingsha Zhang,Zhilong Lin,Xiaolin Ma,Yongke Li,Changlong Wang

doi:10.1155/2021/6360923

Abstract

In this paper, the problem of the delay-dependent robust H ∞ control for a class of uncertain neutral systems with mixed time-varying delays is studied. Firstly, a robust delay-dependent asymptotic stability criterion is shown by linear matrix inequalities (LMIs) after introducing a new Lyapunov–Krasovskii functional (LKF). The LKF including vital terms is expected to obtain results of less conservatism by employing the technique of various efficient convex optimization algorithms and free matrices. Then, based on the obtained criterion, analyses for uncertain systems and H ∞ controller design are presented. Moreover, on the analysis of the state-feedback controller, different from the traditional method which multiplies the matrix inequality left and right by some matrix and its transpose, respectively, we can obtain the state-feedback gain directly by calculating the LMIs through the toolbox of MATLAB in this paper. Finally, the feasibility and validity of the method are illustrated by examples.

Highlights

Speaking, some degrees of time delays are frequently encountered in almost all practical engineering systems such as [1,2,3], in which the existence of the delays may lower the performances of these engineering control systems and even result in the instability of such control systems. en, it is an essential requirement to investigate the stability for systems with time delays
Results about stability analysis for neutral systems with mixed delays (NSMDs) have been obtained in recent years
Motivated by the discussions above, the problem of delay-dependent robust H∞ control of uncertain neutral systems with mixed time-varying delays is explored in this article

Summary

Introduction

Some degrees of time delays are frequently encountered in almost all practical engineering systems such as [1,2,3], in which the existence of the delays may lower the performances of these engineering control systems and even result in the instability of such control systems. en, it is an essential requirement to investigate the stability for systems with time delays. Time-varying delays existed in the longrange or flexible communication channel [26]; the problem of stability of teleoperation systems for timevarying delays by neutral LMI techniques was discussed in [25]. Motivated by the discussions above, the problem of delay-dependent robust H∞ control of uncertain neutral systems with mixed time-varying delays is explored in this article. (4) ough similar papers concerning the delay-dependent robust control of uncertain neutral systems with mixed time-varying delays have already been many, there are some differences between the current submission and latest works. To the extent of the authors’ knowledge, none of the existing works including all the terms of robust control, neutral systems, uncertainties, and mixed time-varying delays derived from actual engineering problems. L2[0, ∞] refers to the space of square integral vectors

Description of the Problem

Main Results

Numerical Examples

Conclusion