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Asymptotic stability and the method of linear bounds

Asymptotic stability and the method of linear bounds

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If = Ax is asymptotically stable, it is possible to find linear bounds for g(x); so that = Ax + g(x) is also asymptotically stable. An explicit expression is given for functions which satisfy these bounds.

References

    1. 1)
      • S. Barnett , C. Storey . Stability analysis of constant linear systems by Lyapunov's second method. Elecrronics Letters
    2. 2)
      • W. Hahn . (1963) , Theory and application of Lyapunov's direct method.
    3. 3)
      • Nesbit, R.A.: `The use of the technique of linear bounds for applying the direct method of Liapunov to a class of non-linear and time-varying systems', Proceedings of the 2nd IFAC congress, 1963, Basle.
    4. 4)
      • Lehnigk, S.G.: `On Liapunov's second method with parameter-dependent quadratic forms in the case of autonomous non-linear equations which have a linear part', Proceedings of the 1st IFAC congress, 1960, Moscow, p. 934.
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