Delay-Dependent Robust H∞ Performance for Uncertain Neutral Systems with Mixed Time-Varying Delays and Nonlinear Perturbations

Kanit Mukdasai,Piyapong Niamsup,Thongchai Botmart,Luu Thi Hiep,Peerapongpat Singkibud

doi:10.1155/2018/5721695

Kanit Mukdasai, Piyapong Niamsup + Show 3 more

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https://doi.org/10.1155/2018/5721695

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Abstract

This paper deals with the problems of delay-dependent stability and H∞ performance for uncertain neutral systems with time-varying delays, and nonlinear perturbations. The time-varying delays are neutral, discrete, and distributed time-varying delays that the upper bounds for the delays are available. The restrictions on the derivatives of the discrete and distributed time-varying delays are removed, which mean that a fast discrete time-varying delay is allowed. The uncertainties under consideration are nonlinear time-varying parameter perturbations and norm-bounded uncertainties, respectively. Firstly, by applying a novel Lyapunov-Krasovskii functional approach, Wirtinger-based integral inequality, Peng-Park’s integral inequality, decomposition technique of constant matrix, descriptor model transformation, Leibniz Newton formula and utilization of zero equation, and improved delay-dependent bounded real lemmas (BRL) for systems are established in terms of linear matrix inequalities (LMIs). Then, based on the obtained BRL, some less conservative delay-dependent stability criteria of uncertain neutral systems with mixed time-varying delays and nonlinear perturbations are obtained and improved H∞ performance criterion with the framework of LMIs is introduced. Finally, some numerical examples are given to illustrate that the presented method is effective.

Highlights

Time delay is frequently a source of instability and a source of generation of oscillation in many dynamic systems such as hybrid systems [1, 2], networked control systems, biological systems, mechanical systems, and chemical or process control systems [3]
By applying a novel LyapunovKrasovskii functional approach, Wirtinger-based integral inequality, Peng-Park’s integral inequality, decomposition technique of constant matrix, descriptor model transformation, Leibniz Newton formula and utilization of zero equation, and improved delaydependent bounded real lemmas (BRL) for systems are established in terms of linear matrix inequalities (LMIs)
The system models can be described by functional differential equation of neutral type, in which the models depend on the state delay and depend on the state derivatives, are often encountered in various fields, such as population ecology [12], distributed networks containing lossless transmission lines [13], heat exchangers, and robots in contact with rigid environments [14]

Summary

Introduction

Time delay is frequently a source of instability and a source of generation of oscillation in many dynamic systems such as hybrid systems (and practical application) [1, 2], networked control systems, biological systems, mechanical systems, and chemical or process control systems [3]. Very recently, improved H∞ performance analysis and stability for uncertain systems with time-varying delays were proposed in [10, 11, 24]. Delay-dependent stability criteria are concerned with the size of the delay and usually provide a maximal delay size. Speaking, the latter ones are less conservative than the former ones when the timedelay values are small. With above motivations, based on Lyapunov stability theory, improved H∞ performance criteria and stability analysis for uncertain neutral systems with mixed timevarying delays and nonlinear perturbations are derived by the framework of LMIs which will be introduced in Theorem 11. Some numerical examples are given to illustrate that the presented method is effective

Problem Formulation

Main Results

Numerical Examples

Method μm

Conclusions