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The optimal regulation properties of multi-input and multioutput (MIMO) discrete-time networked control systems (NCSs), over additive white Gaussian noise (AWGN) fading channels, based on state space representation, are investigated. The average performance index is introduced. Moreover, the regulation performance is measured by the control energy and the error energy of the system, and fundamental limitations are obtained. Two kinds of network parameters, fading and the additive white Gaussian noise, are considered. The best attainable regulation performance limitations can be obtained by the limiting steady state solution of the corresponding algebraic Riccati equation (ARE). The simulation results are given to demonstrate the main results of the theoretical development.

In recent years, there has been growing attention devoted to the study of feedback control over communication networks [

Performance limitation of control systems has been receiving an increasing amount of interest in the control community; see [

In this paper, we investigate optimal regulation performance issues pertaining to MIMO feedback control systems over multiple AWGN fading channels. The average performance index is introduced, and the regulation performance is measured by controlling energy and the state energy of the system. And regulation fundamental limitations are obtained. The stability or stabilization problem for the network with a fading channel is considered in a few works [

The rest of the paper is organized as follows. The feedback regulation performance limitations are studied by parameter controller in Section

In this work, we will consider a feedback control system with a network in the upstream channel as showed in Figure

State feedback control by one-parameter controller over AWGN fading channels.

Assume that the plant

The input and output relationship for the AWGN fading channel is given by

Besides the fading phenomenon, the uncertainties of a digital network can be described by the model (

The following lemmas are useful for subsequent development and thus are introduced first.

The equation

In this subsection, we consider the feedback system of Figure

The problem under study can be described as follows.

For a discrete-time NCS as depicted in Figure

Consider the feedback system of Figure

The optimal problem is formulated in terms of the state covariance matrices

Considering the traditional sense of the performance index

When the unreliable network does not contain the fading channel, that is, it contains only a white Gaussian noise channel, we can obtain the following corollary.

Consider the feedback system of Figure

Similar to the previous section

We now use an example to illustrate Theorem

Figures

In this paper, we have investigated the optimal regulation performance of networked control systems over an unreliable network in the path from the controller to the plant. The unreliable network contains a fading channel and an additive white Gaussian noise (AWGN) channel. We consider two types of feedback control: state feedback and output feedback, and fundamental limitations are obtained for regulation performance, respectively. The optimal regulation performance limitations can be obtained by the limiting steady state solution of its associated algebraic Riccati equation (ARE). Finally, some simulation results are given to illustrate the obtained results.

Furthermore, the obtained results of this paper can be easily extended to the continuous-time case. When the networked control system contains the nondeterministic or hybrid switching, the issue of performance limitation also deserves to be studied furthermore.

The authors declare that they have no competing interests.

This work is partially supported by the National Natural Science Foundation of China (61503133, 61374171, 51374107, and 51577057), by Major State Basic Research Development Program (973) subproject (61325309), by the Research Foundation of Education Bureau of Hunan Province (15C0548), by the Province Natural Science Foundation of Hunan under Grants 2016JJ6043 and 14JJ3110, and by the Postdoctoral Science Foundation of China under Grant 2016M592449.