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This paper deals with the problem of guaranteed cost control for a class of nonlinear networked control systems (NCSs) with time-varying delay. A guaranteed cost controller design method is proposed to achieve the desired control performance based on the switched T-S fuzzy model. The switching mechanism is introduced to handle the uncertainties of NCSs. Based on Lyapunov functional approach, some sufficient conditions for the existence of state feedback robust guaranteed cost controller are presented. Simulation results show that the proposed method is effective to guarantee system’s global asymptotic stability and quality of service (QoS).

As network technology advanced in the last decade, networked control system (NCS) has increasingly become a research focus. Considerable attention on the modeling and controller design of NCSs has been paid in [

However, due to the insertion of communication channels, this brings many challenging problems such as network-induced delay and data packet dropout. Regardless of the type of network used, these special issues degrade the system dynamic performance and are a source of potential instability. There are a number of design methods that have been proposed to deal with these problems. One of the most general methods is to model the NCS as a system with time-varying delays. So the stability of an NCS is equivalent to the stability of a system with time-varying delays [

In the last few years, the fuzzy control is a useful approach to solve the control problems of nonlinear systems. The Takagi-Sugeno (T-S) fuzzy system proposed in [

Nevertheless, an inherent drawback remains since the number of fuzzy rules of a T-S model increases exponentially with the number of nonlinearities constituting the matched nonlinear system [

In designing a controller for a real plant, it is invariably necessary to design a control system which not only is stable but also possesses a strong robust performance. One way to deal with this is the so-called guaranteed cost control approach [

In this paper, we aim at the problem of guaranteed cost control for a class of uncertain nonlinear NCSs with time delays. Considering the QoS of NCSs, we propose a guaranteed cost control scheme to achieve the desired control performance based on switched T-S fuzzy control method, where the switching mechanism is introduced to handle the uncertainties. Moreover, the sufficient condition for the existence of the robust guaranteed cost controller and the design method of the corresponding switching control law are obtained via Lyapunov functions. Comparing with [

The innovations of this paper are as follows: (1) the guaranteed cost controller is proposed for nonlinear NCSs with time-varying delay to achieve the desired control performance based on the switched T-S fuzzy model with uncertain parameters, and (2) the sufficient condition for the robust guaranteed cost control law is presented to uncertain nonlinear NCSs.

The paper is organized as follows. The basic problem formulation of the nonlinear networked control system is given in Section

A general NCS configuration is illustrated in Figure

A general NCS.

In Figure

Before designing the controller, we make the following reasonable assumptions.

The sensor is clock-driven. The controller and actuator are event-driven. The clocks among them are synchronized.

Time-varying network-induced delay is less than one sampling period.

The computational delay is negligible.

The signal is single-packet transmission without packet drop.

Assuming the node sampling period is

Furthermore, (

The guaranteed cost function associated with system (

Consider the uncertain system (

We assume that switched fuzzy controller is constituted with

When the controlled system is in

For a given symmetric matrix,

Given matrices

Consider the uncertain nonlinear networked control systems (

For the networked control system (

Thus

Thus, if the matrix inequalities (

Let

Define sets

Obviously, we have

Construct a switching law as follows:

Notice that

Consider the uncertain nonlinear networked control systems (

By the Lemmas

Without loss of generality, we assume that

Obviously, there exists at least one

Let

Construct the sets

Obviously, we have

Construct a switched law by

Thus, from (

Following the similar lines as in the proof of Theorem

Consider the nonlinear system with the following differential equation [

Choose the state variable and the input variable as

The sampling period

The membership function of input

Suppose the switched fuzzy feed-back controllers are the following fuzzy controllers:

Choose

Figures

The state trajectory using fuzzy controller 1.

The state trajectory using fuzzy controller 2.

The state trajectory using switched fuzzy controller.

In this paper, we have presented a novel controller design methodology for a class of nonlinear NCSs based on switched T-S fuzzy model. By introducing the switching mechanism into the fuzzy T-S systems, the proposed methods can deal with the uncertainties of nonlinear NCSs with time delays and furthermore avoid the inherent drawback of a fuzzy T-S model in controller design and implementation of nonlinear systems. In addition, considering QoS of nonlinear NCSs, some sufficient conditions for the existence of the robust guaranteed cost control law have been built via Lyapunov functional approach. Simulation results have verified and confirmed the effectiveness of the guaranteed cost controller based on the switched T-S fuzzy model for nonlinear NCSs.

At present, this paper only presents a numerical example to show the validity of our control scheme on the nonlinear NCS with time delays. In next step, we plan to further verify this control scheme via practical NCSs and investigate the stability analysis and controller design with multiple-packet transmission in nonlinear NCSs. Moreover, the boundedness of the parameter constraints for NCSs will be studied. The switched dynamics of nonlinear NCSs will also be considered in future investigation.

The authors declare that there is no conflict of interests regarding the publication of this paper.

This work is supported by National Natural Science Foundation of China (Grant no. 50804061) and Scientific and Technological Research Program of Chongqing Municipal Education Commission (Grant no. KJ130522).