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Continuous output-feedback stabilization for a class of stochastic high-order nonlinear systems

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Abstract

This paper is concerned with the global stabilization via output-feedback for a class of high-order stochastic nonlinear systems with unmeasurable states dependent growth and uncertain control coefficients. Indeed, there have been abundant deterministic results which recently inspired the intense investigation for their stochastic analogous. However, because of the possibility of non-unique solutions to the systems, there lack basic concepts and theorems for the problem under investigation. First of all, two stochastic stability concepts are generalized to allow the stochastic systems with more than one solution, and a key theorem is given to provide the sufficient conditions for the stochastic stabilities in a weaker sense. Then, by introducing the suitable reduced order observer and appropriate control Lyapunov functions, and by using the method of adding a power integrator, a continuous (nonsmooth) output-feedback controller is successfully designed, which guarantees that the closed-loop system is globally asymptotically stable in probability.

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Authors and Affiliations

  1. School of Control Science and Engineering, Shandong University, Jinan Shandong, 250061, China

    Jian Zhang & Yungang Liu

  2. Department of Mathematics, Zhengzhou University, Zhengzhou Henan, 450001, China

    Jian Zhang

Authors
  1. Jian Zhang
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  2. Yungang Liu
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Corresponding author

Correspondence to Yungang Liu.

Additional information

This work was supported by the National Natural Science Foundations of China (Nos. 60974003, 61143011, 61273084, 61233014), the Natural Science Foundation for Distinguished Young Scholar of Shandong Province of China (No. JQ200919), and the Independent Innovation Foundation of Shandong University (No. 2012JC014).

Jian ZHANG received his Ph.D. degree in Control Theory and Control Engineering from Shandong University in 2012. He is currently a lecture at the Department of Mathematics, Zhengzhou University. His research interests include nonlinear system control design, stochastic control and adaptive control theory.

Yungang LIU received his Ph.D. degree in Control Theory and Applications from Shanghai Jiao Tong University in 2000. During 2001 to 2003, he worked as a postdoctoral scholar at Academy of Mathematics and Systems Science. He is currently a professor at the School of Control Science and Engineering, Shandong University. He is the recipient of the 10th Guan Zhao-Zhi Award. He serves on the IEEE Control Systems Society Conference Editorial Board, and is an associate editor of Acta Automatica Sinica. His research interests include stochastic control, nonlinear control design and system analysis, adaptive control and applications in smart grid.

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Zhang, J., Liu, Y. Continuous output-feedback stabilization for a class of stochastic high-order nonlinear systems. J. Control Theory Appl. 11, 343–350 (2013). https://doi.org/10.1007/s11768-013-2166-z

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  • DOI: https://doi.org/10.1007/s11768-013-2166-z

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