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The observer-based decentralized control problem is investigated for a class of uncertain interconnected systems of neutral type. Using the singular value decomposition approach, a full-order observer is designed to guarantee the asymptotic stability of the error dynamic system. A novel mathematical technique is developed to solve this design problem. Sufficient condition for uncertain interconnected systems of neutral type to be asymptotic stable is established based on the singular value decomposition method. Furthermore, the desired gains of observer and controller are obtained by the explicit expressions in terms of some free parameters. Finally, an illustrative example is used to demonstrate the proposed approach, and the corresponding simulation results are given to elucidate the effectiveness.

Nowadays the systems have become more and more large, and for the interconnected systems decentralized control has obvious advantage that overcomes the limitations of the traditional centralized control requiring sufficiently large communication bandwidth to exchange information between the subsystems. Therefore, the decentralized control scheme [

On the other hand, the neutral system is the general form of delay system that contains the same highest order derivatives for the state vector

Furthermore, Ma et al. [

Nowadays, observer control is also an attractive topic [

To the best of the authors’ knowledge, the observer-based decentralized control problems of uncertain interconnected systems with neutral type have not yet been investigated, which motivates the present study. In this paper, the asymptotic stabilization of a class of uncertain neutral interconnected systems with time-varying delays in state, control input, and interconnections is made. In framework of linear matrix equalities, the design of the observer and controller is formulated. Sufficiently the influence of interconnections on the system performance is taken into account, and interconnections are dealt with by flexible techniques. These strategies allow one to obtain less conservative stabilization conditions. A numerical example and the corresponding simulation results are given to illustrate the effectiveness of the proposed method of decentralized controller based on observer.

The remainder of the paper is organized as follows. The observer-based decentralized control problem formulation is described in Section

Consider the following uncertain neutral interconnected systems composed of

Time-varying parametric uncertainties

The following assumptions are made on the considered system (

Suppose that the matrix

The matrix

Consider the following observer-based decentralized control for system (

Consider system (

For a given

where

Consider uncertain neutral interconnected systems (

then system (

According to Schur complement, inequality (

where

By Lemma

where

Pre- and postmultiplying matrix

Construct the following Lyapunov functional candidate:

For the system (

By some simple derivations, the time derivative of

According to conditions (

In addition, Assumption

One of the distinctive features of this paper is that the

Consider system (

Applying Matlab toolbox to solving inequality (

Under the following initial condition

State responses of the first closed-loop subsystem.

State responses of the second closed-loop subsystem.

The control signals of the first subsystem.

The control signals of the second subsystem.

Output responses of the first subsystem.

Output responses of the second subsystem.

State responses of the first observer subsystem.

State responses of the second observer subsystem.

Output responses of the first observer subsystem.

Output responses of the second observer subsystem.

State responses of the first error subsystem.

State responses of the second error subsystem.

The simulations results indicate that the designed observer can stabilize the error dynamic system and estimate the states of the interconnected systems of neutral type.

For this example,

The observer-based decentralized control problem of uncertain interconnected systems of neutral type is complex and challenging. In framework of Lyapunov stability theory, a novel mathematical technique to deal with the parametric disturbances is developed to obtain the sufficient conditions of existing anticipated controller and observer. The sufficient conditions are the coupled LMIs and depend on not only the sizes of delays, but also the information of derivatives. The numerical example and the corresponding simulation results elucidate that the results obtained in this paper are effective.

This research is supported by the Natural Science Foundation of China (no. 61104106), the Science Foundation of Department of Education of Liaoning Province (no. L2012422), and the Doctorial Science Foundation of Shenyang University (no. 20212340).