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In this paper, the absolute stability for a class of switched delay systems with time-varying uncertainties is analyzed. By constructing an appropriate Lyapunov-Krasovskii functional, a new and less conservative criterion is proposed based on the MDADT method. Besides, the idea of

Switched system is an important class of hybrid system which can be described by a series of continuous or discrete subsystems with a rule organizing the switching among them. As well known, many kinds of practical systems, such as power systems and chemical procedure control systems, may be properly modeled by the switched systems [

Apart from that, in many physical systems, such as chemical process and electric network, time-delay phenomenon is also unavoidable. Time-delays may lead to instability or even poor performance such as chaos [

Consequently, the stability of switched systems with time delay is worth considering. In fact, switched delay systems have a wide range of practical backgrounds in network control [

In addition, since it was raised in 1940s, Lur’e systems have been deeply concerned. The main concern of Lur’e systems is absolute stability which covers systems without delays and those with delays [

Integrated with the features of switched systems and Lur’e systems, switched Lur’e systems have also been paid much attention. A number of systems in control communities can be modeled by switched Lur’e systems, such as Hopfield neural network [

Recently, [

In this paper, the absolute exponential stability of switched Lur’e systems with delays is investigated. The main contribution of this paper is as follows.

The rest of this paper is organized as follows. The problem is stated in Section

Consider the following system

System described by (

For a switching signal

For any symmetric positive definite matrix

For given matrices

In the previous work [

Inspired by the method in [

As in [

For given

Differentiating function (

By Schur complement, it yields that

When

For given

In fact, Corollary

In fact, if we set

Similarly, when

For given

Using the transform in [

Except the absolute stability of system (

For system (

For given

Replacing

The results of this paper are based on LMI technology. In further research, when nonconvex matrix inequality conditions (nonlinear coupling) are encountered, the Chang-Yang decoupling method ([

Consider uncertain system (

Switching signal.

The response curve of the states in example.

Table

Comparison with the result in [

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Corollary 2 [ | 2.2845 | 2.2352 | 2.0243 |

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Corollary | 3.0079 | 2.6738 | 2.1654 |

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Corollary | 3.1085 | 2.7602 | 2.4731 |

In this article, we considered the stability of switched Lur’e systems. In order to derive less conservative criteria, we introduce an appropriate Lyapunov-Krasovskii functional by the method of delay length segmentation ([

The data used to support the findings of this study are included within the article.

The authors declare that they have no conflicts of interest.

This research is supported by the National Natural Science Foundation of China (11171131) and Jilin Provincial Natural Science Foundation of China (201115043).