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This paper investigates nonfragile

As we all known, in practical control systems, nonlinearity and time delay phenomena are often encountered in various industry and control system, such as networked control system and mechanical drive control system. The control of nonlinear systems has been explored and studied by many scholars in related fields. T-S fuzzy model is a powerful tool to deal with nonlinearity; much effort has been devoted on the networked control system for T-S fuzzy system or time-delayed (see [

However, in practical system, it is difficult for an exactly implemented filter to meet the actual requirements because inaccuracies or uncertainties, which include collection error and component aging, may occur during filter implementation. It often degrades the performance of the control system and even instability; the filter has a higher sensitivity to the parameter uncertainty [

Motivated by the aforementioned discussion, in this paper, a nonfragile

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

Consider a nonlinear system with time-varying delay which could be approximated by a class of T-S fuzzy systems with time-varying delays. The T-S fuzzy model with plant rules can be described by the following.

By employing the commonly used center-average defuzzifier, product interference, and singleton fuzzifier, the overall fuzzy model is inferred as follows:

where

Consider the nonfragile fuzzy filter with multiplicative gain uncertainties; we design the following fuzzy

Consider the following

The multiplicative gain uncertainties are defined as

By combining (

In this paper, our purpose is to design the fuzzy

The purpose of this paper is to design nonfragile

Let

For any vectors

Let

Let

Suppose

For nonlinear systems (

We construct a novel Lyapunov-Krasovskii function as follows:

By Lemma

Similar to (

By Lemma

Similar to (

Combining with inequalities (

Lemma

where

By Lemma

By Lemma

By Lemma

Combining with formulas (

Similarly, for formula (

By Lemma

Combining with formulas (

where

By Schur complement and formula (

where

Consequently, it follows from inequality (

Thus,

Theorem

For given scalars

We can obtain the filter parameters as follows:

By Schur complement formula, the matrix inequality conditions (

Let

According to

Consider the following nonlinear systems with time-varying delays:

where

The known matrices in (

The disturbance signal

We can get the desired nonfragile filter by solving LMIS (

In addition, the new method provides less conservative design result; we can obtain a smaller

The response curve of system states

The response curve of system states

The response curve of vector

The response curve of vector

The random disturbance signal is given as follows:

The event occurrence probability

The response curve of system states

The response curve of system states

The response curve of vector

The response curve of vector

The stochastic variables

The results show that the

This paper studied the fuzzy nonfragile

The data used to support this study are currently under embargo while the research findings are commercialized. Requests for data, 12 months after initial publication, will be considered by the corresponding author.

The authors declare that there are no conflicts of interest regarding the publication of this paper.

This work was supported in part by Science and Technology project of State Grid corporation of China (SGTYHT/13-JS-175).

_{∞}filter design for nonlinear systems with time-delay through T-S fuzzy model approach