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Critical stability and stabilization of discrete-time stochastic systems and its applications

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  • Control Theory
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Abstract

In this paper, critical stability and critical stabilization for discrete stochastic systems with both state and control dependent noise are discussed via the spectrum technique. The Popov-Belevitch-Hautus (PBH) criterion for exact observability in a discrete version is presented. As applications, some interesting results on a class of generalized Lyapunov equations (GLE), unremovable spectra and discrete generalized algebraic Riccati equation (GARE) are obtained. Finally, the problem of assigning the spectra of discrete stochastic systems in a specified disk is considered and some numerical examples are given to demonstrate our results.

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Authors and Affiliations

  1. College of Information and Electrical Engineering, Shandong University of Science and Technology, Qingdao, Shandong, 266510, China

    Huiying Sun, Meng Li & Weihai Zhang

Authors
  1. Huiying Sun
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  2. Meng Li
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  3. Weihai Zhang
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Corresponding author

Correspondence to Huiying Sun.

Additional information

Recommended by Editorial Board member Young Soo Suh under the direction of Editor Young Il Lee.

This work was supported by the National Natural Science Foundation of China (Grant No.60874032), the Key Project of Natural Science Foundation of Shandong Province(Grant No. ZR2009GZ001) and the Specialized Research Fund for the Doctoral Program of Higher Education of PR China (Grant No. 20103718110006). The authors would like to thank the Editor Young Il Lee and Editorial Board member Young Soo Suh.

Huiying Sun received her M.S. degree from Qingdao University of Science and Technology, and her Ph.D. degree from the Ocean University of China, in 2004 and 2007, respectively. She is currently an associate professor of Shandong University of Science and Technology. Her main research interests include optimal control and linear stochastic control.

Meng Li received his Bachelor degree majoring in Communication Engineering from Shandong University of Science and Technology, China, in 2008. Since September 2008, he has been pursuing his M.S. degree in the same University. His main research interests include linear stochastic control and stochastic differential games.

Weihai Zhang received his M.S. degree from Hangzhou University, and his Ph.D. degree from Zhejiang University, Hangzhou, China, in 1994 and 1998, respectively. From August 1998 to May 2001, he worked at Shandong Institute of Light Industry as an associate professor. He was a postdoctoral researcher from May 2001 to July 2003 at National Tsing Hua University, Hsinchu, Taiwan. He rejoined Shandong Institute of Light Industry in August 2003 as a professor. From November 2006 to May 2007, he visited Nanyang Technological University as a visiting research scientist. He is currently a professor of Shandong University of Science and Technology. His research interests include linear and nonlinear stochastic optimal control, robust H infinity control and stochastic stability.

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Sun, H., Li, M. & Zhang, W. Critical stability and stabilization of discrete-time stochastic systems and its applications. Int. J. Control Autom. Syst. 9, 1028–1036 (2011). https://doi.org/10.1007/s12555-011-0602-8

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  • DOI: https://doi.org/10.1007/s12555-011-0602-8

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