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Some problems associated with the disturbed matrix Lyapunov equation for linear time-invariant discrete systems

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Abstract

Both the Lyapunov stability and Popov's hyperstability of discrete linear time-invariant system in case of system parameter disturbance are discussed in this paper. The allowable disturbance ranges are given so that the maintenance of the Lyapunov stability and the Popov's hyperstability of a discrete linear system is guaranteed. The results find their significance in the MRAC.

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References

  1. Hwang Ling,Linear Algebra in System and Control Theory (to be published), Science Press, Beijing, (in Chinese).

  2. Narendra, K. S.,Adaptive Control — MRAC, Lecture Notes of the Lecture Delivered in Nanjing Institute of Technology, Sept. (1981).

  3. Narendra, K. S. and L. S. Valavani,A comparison of Lyapunov and hyperstability approaches of adaptive control of continuous systems, IEEE Trans. on Ac-25, (1980).

  4. Anderson, B. D. O.,A simplified viewpoint of hyperstability, IEEE Trans. on AC-13, (1968).

  5. Kalman, R. E.,Lyapunov function for the problem of Lure in automatic control, Proc. of the NAS of the U.S.A., (1963).

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  8. Zhu Wei-ling and Hwang Ling,Some problems concerning the hyperstability theory in design of adaptive control, Proceedings of the Biannual Meeting on Control Systems, Shanghai, (1981).

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Authors and Affiliations

  1. Mechanics Department, Peking University, Peking, China

    Hwang Ling & Zhu Wei-ling

Authors
  1. Hwang Ling
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  2. Zhu Wei-ling
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Communicated by Zhu Zhao-xiang.

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Ling, H., Wei-ling, Z. Some problems associated with the disturbed matrix Lyapunov equation for linear time-invariant discrete systems. Appl Math Mech 4, 97–106 (1983). https://doi.org/10.1007/BF01896717

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  • DOI: https://doi.org/10.1007/BF01896717

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