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Mean square detectability of LTI systems over finite-state digital block-fading channels

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  • Control Theory and Applications
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Abstract

This paper studies the mean square quadratic (MSQ) detectability for multi-output networked systems over finite-state digital block-fading channels. The packet-loss rate of each digital fading channel depends on the channel power gain, as well as packet length and power level used for transmission. A finite-state random process is introduced to model time-varying fading channels, which characterizes various configurations of physical communication environment and/or different channel fading amplitudes. Necessary and sufficient conditions for MSQ detectability over finite-state Markov digital block-fading channels are given in the form of algebraic Riccati equations or linear matrix inequalities (LMIs). The estimation gain is given as a function of estimated/observed channel state. In addition, explicit conditions on network for MSQ detectability over finite-state independent identically distributed (i.i.d.) digital block-fading channels are presented in terms of the unstable poles of the multi-output plant. Finally, an application to Gilbert-Elliott channels (GECs) is provided to demonstrate the derived results.

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Authors and Affiliations

  1. Key Laboratory of Advanced Control and Optimization for Chemical Process (East China University of Science and Technology), Ministry of Education, Shanghai, 200237, China

    Wei Chen, Yuanyuan Zou & Yugang Niu

  2. School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore, 639798, Singapore

    Nan Xiao

Authors
  1. Wei Chen
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  2. Yuanyuan Zou
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  3. Nan Xiao
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  4. Yugang Niu
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Corresponding author

Correspondence to Yuanyuan Zou.

Additional information

Recommended by Associate Editor Young Soo Suh under the direction of Editor PooGyeon Park. This work was supported by National Natural Science Foundation (NNSF) from China (61374107, 61673174, 61304044).

Wei Chen is currently pursuing an M.E. degree in control science and engineering in East China University of Science and Technology. His research interests include networked control systems and multi-agent systems.

Yuanyuan Zou received her Ph.D. degree from Shanghai Jiao Tong University in 2009. Her research interests include predictive control, network-based control systems and distributed control systems.

Nan Xiao received his Ph.D. degree in electrical and electronic engineering from Nanyang Technological University, Singapore, in 2012. His current research interests include networked control systems, multi-agent systems, transportation networks, and game theory.

Yugang Niu received the Ph.D. degree in Control Theory and Control Engineering Automation from Nanjing University of Science and Technology in 2001. His research interests include nonlinear control, stochastic control systems, sliding mode control and network congestion control.

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Chen, W., Zou, Y., Xiao, N. et al. Mean square detectability of LTI systems over finite-state digital block-fading channels. Int. J. Control Autom. Syst. 15, 498–505 (2017). https://doi.org/10.1007/s12555-015-0283-9

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  • DOI: https://doi.org/10.1007/s12555-015-0283-9

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