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This paper presents the decentralized trackers using the observer-based suboptimal method for the interconnected time-delay singular/nonlinear subsystems with closed-loop decoupling property. The observer-based suboptimal method is used to guarantee the high-performance trajectory tracker for two different subsystems. Then, due to the high gain that resulted from the decentralized tracker, the closed-loop system will have the decoupling property. An illustrative example is given to demonstrate the effectiveness of the proposed control structure.

The singular system model is a natural presentation of dynamic systems, such as power systems [

In the recent years, a large number of control systems are characterized by interconnected large-scale subsystems, and many practical examples have been applied to decentralized control systems. The decentralized control of interconnected large-scale systems has commonly appeared in our modern technologies, such as transportation systems, power systems, and communication systems [

In this paper, we consider the time-delay effect. In practical applications, the time-delay effect [

This paper is organized as follows. Section

Consider the time-delay system consisting of two interconnected MIMO subsystems shown as

The subsystem

The schematic design methodology for the interconnected time-delay singular/nonlinear system.

It is very difficult to directly design the tracker and observer for

We will use the proposed schematic design in Figure

In this section, we construct the methodology of the decentralized control by using the design concept of the observer-based suboptimal digital tracker to control time-delay singular subsystem and time-delay nonlinear subsystem, respectively. Before designing the controller, we need to obtain the equivalent time-delay linear nonsingular subsystem and the equivalent time-delay linear subsystem. The problem of decentralized stabilization is discussed in the appendix.

From the schematic design methodology of Figure

Notably, definitions of the regular pencil [

Similarly, the time-delay nonlinear subsystems (

The equivalent subsystems (

Consider the continuous time-delay singular subsystems (

Consider the continuous time-delay singular subsystems (

Similarly, some terms in (

In the following work, we use (

By the previous method [

The decentralized control for the interconnected time-delay singular/nonlinear subsystems.

From Figures

Perform the previously proposed method [

Design the observer-based suboptimal digital trackers from the equivalent time-delay linear subsystems obtained in Step

Perform the observer-based suboptimal digital trackers obtained in Step

Consider the time-delay system consisting of two interconnected MIMO subsystems shown as

The second subsystem

Two-link robot.

The dynamic equation of the two-link robot system can be expressed as follows:

Let

Calculate the inverse of the matrix

Combining the above systems with the nonlinear interconnected terms, the large-scale system can then be shown in Figures

Based on Section

Following the proposed method in this paper, let the reference inputs

(a) Output responses of the subsystem

(a) Output responses of the subsystem

In order to confirm the independence of the control for the two subsystems, the time-varying optimal digital controller of the subsystem

The unanticipated failure occurs without fault-tolerant control during

The unanticipated failure occurs without fault-tolerant control during

To show the effectiveness of the proposed method, we compare it with the observer/Kalman filter identification (OKID) method in the simulation for the subsystem

(a) The comparison between the system output

(a) The comparison between the system output

From the comparison between Figures

This paper presents a systematical methodology of the decentralized control for the interconnected time-delay singular/nonlinear subsystems with closed-loop decoupling property. We use the observer-based suboptimal digital tracker with high gain property to keep the good tracking performance. Moreover, the decoupling property performs very well such that even if some unanticipated fault occurs in some of subsystems, it still will not affect the tracking performance of each subsystem. The proposed methods depend on the decentralized modeling of the interconnected sampled-data time-delay subsystems in Section

The necessary and sufficient conditions for the decentralized stabilization are presented in [

Consider the given system

Consider system

Necessary and sufficient condition for the existence of a decentralized feedback control law for the system

We first establish necessity. Assume local controllers

Next, we establish sufficiency. To prove that we can actually stabilize the system, we use a recursive argument. Assume the system has an unstable eigenvalue in

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

The authors would like to thank the National Science Council of the Republic of China, Taiwan, for financially supporting this research under Contract no. NSC 101-2511-S-197-002.