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Stability of lurie-type non-linear equations

  • Alfredo S. Somolinos
Article

Summary

Conditions are given for the indirect control system x′=a(x)+bμ, μ′=φ(σ), σ=cTx−ϱμ, to be absolutely stable. These conditions reduce to LaSalle and Lefschetz's in the linear case: a(x)=Ax. The conditions obtained for the stability of the direct control system x′=a(x)+bφ(σ), σ=cTx, reduce also to Lurie's condition in the linear case. The case of the direct control system x′=a(x, t)+bφ(σ), σ=cTx is also investigated.

Keywords

Control System Direct Control Linear Case Indirect Control Indirect Control System 

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References

  1. [1]
    M. Aizerman — F. R. Gantmacher,Absolute stability of control systems, Russian (1963), English Translation, Holden-Day, San Francisco (1963).Google Scholar
  2. [2]
    E. A. Barbashin,Funktsii Ljapunova, Nauka, Moskva (1970).Google Scholar
  3. [3]
    N. P. BhatiaG. P. Szegö,An extension theorem for asymptotic stability, inDifferential Equations and Dynamical Systems,J. Hale andJ. P. LaSalle (editors), Academic Press, New York (1967).zbMATHGoogle Scholar
  4. [4]
    A. Halanay,Differential equations, Stability, Oscillation, Time Lags, Academic Press, New York (1966).zbMATHGoogle Scholar
  5. [5]
    P. Hartman,Ordinary Differential Equations, John Wiley, New York (1964).zbMATHGoogle Scholar
  6. [6]
    J. P. LaSalleS. Lefschetz,Stability by Liapunov's Direct Method with Applications, Academic Press, New York (1961).zbMATHGoogle Scholar
  7. [7]
    A. M. Letov,Stability of Nonlinear Controls, Princeton University Press, Princeton, New Jersey (1961).CrossRefGoogle Scholar
  8. [8]
    J. L. Willems,Stability Theory of Dynamical Systems, John Wiley and Sons, New York (1970).zbMATHGoogle Scholar
  9. [9]
    T. Yoshizawa,Stability theory by Liapunov's second method, The Mathematical Society of Japan (1966).Google Scholar

Copyright information

© Fondazione Annali di Matematica Pura ed Applicata (1923 -) 1978

Authors and Affiliations

  • Alfredo S. Somolinos
    • 1
  1. 1.Providence

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