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On stability of random Riccati equations

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Abstract

Random Riccati equations (RRE) arise frequently in filtering, estimation and control, but their stability properties are rarely rigorously explored in the literature. First a suitable stochastic observability (or excitation) condition is introduced to guarantee both theL r- and exponential stability of RRE. Then the stability of Kalman filter is analyzed with random coefficients, and theL r boundedness of filtering errors is established.

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References

  1. Anderson, B. D. O., Moore, J. B.,Optimal Filtering, Englewood Cliffs: Prentice-Hall, 1979.

    MATH  Google Scholar 

  2. Deyst, J. J., Price, C. F., Conditions of asymptotic stability of the discrete minimum-variance linear estimator,IEEE Trans. Automat. Contr., 1968, 13: 702.

    Article  MathSciNet  Google Scholar 

  3. Guo, L., Estimating time-varying parameters by the Kalman filter based algorithm: stability and convergence,IEEE Trans. Automat. Contr., 1990, 35(2): 141.

    Article  MATH  Google Scholar 

  4. Guo, L., Stability of recursive stochastic tracking algorithms,SIAM J. Control and Optimization, 1994, 32(5): 1195.

    Article  MATH  MathSciNet  Google Scholar 

  5. Solo, V., Stability of the Kalman filter with stochastic time-varying parameters,Proc. of the 35th IEEE-CDC, Kobe, Japan, December, 1996.

  6. Bougerol, P., Kalman filtering with random coefficients and contractions,SIAM J. Control and Optimization, July 1993, 31 (4): 942.

    Article  MATH  MathSciNet  Google Scholar 

  7. Chen, H. F., Guo, L.,Identification and Stochastic Adaptive Control, Boston: Birkhauser, 1991.

    Book  MATH  Google Scholar 

  8. Guo, L.,Time-Varying Stochastic Systems: Stability, Estimation and Control (in Chinese), Changchun: Jilin Science and Technology Press, 1991.

    Google Scholar 

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Authors and Affiliations

  1. Institute of Systems Science, Chinese Academy of Sciences, 100080, Beijing, China

    Yuan Wang & Lei Guo

Authors
  1. Yuan Wang
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  2. Lei Guo
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Wang, Y., Guo, L. On stability of random Riccati equations. Sci. China Ser. E-Technol. Sci. 42, 136–148 (1999). https://doi.org/10.1007/BF02917108

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  • DOI: https://doi.org/10.1007/BF02917108

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