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Stability analysis and optimal control of stochastic singular systems

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Abstract

In this paper, problems of stability and optimal control for a class of stochastic singular systems are studied. Firstly, under some appropriate assumptions, some new results about mean-square admissibility are developed and the corresponding LMI sufficient condition is given. Secondly, finite-time horizon and infinite-time horizon linear quadratic (LQ) control problems for the stochastic singular system are investigated, in which the coefficients are allowed to be random in control input and quadratic criterion. Some results involving new stochastic generalized Riccati equation are discussed as well. Finally, the proposed LQ control model for stochastic singular systems provides an appropriate and effective framework to study the portfolio selection problem in light of the recent development on general stochastic LQ problems.

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Acknowledgments

This work was supported by National Natural Science Foundation of China under Grant No.60974004 and under Grant No. 61273008.

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Authors and Affiliations

  1. Institute of Systems Science, Northeastern University, Shenyang, 110189, Liaoning, China

    Qingling Zhang & Shuangyun Xing

  2. College of Science, Shenyang Jianzhu University, Shenyang, 110168, Liaoning, China

    Shuangyun Xing

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  1. Qingling Zhang
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  2. Shuangyun Xing
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Correspondence to Qingling Zhang.

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Zhang, Q., Xing, S. Stability analysis and optimal control of stochastic singular systems. Optim Lett 8, 1905–1920 (2014). https://doi.org/10.1007/s11590-013-0687-5

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  • DOI: https://doi.org/10.1007/s11590-013-0687-5

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