Generalisation of Zubov's construction procedure for Lyapunov functions

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Generalisation of Zubov's construction procedure for Lyapunov functions

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© The Institution of Electrical Engineers
Published

This letter presents a method by which Lyapunov functions can be generated for an n-dimensional nonlinear system. Recursive relationships are derived for the coefficients of a multidimensional power series which are a generalisation of the results of Margolis and Vogt. The solutions for the higher-order coefficients of the series incorporate some useful extensions of the concept of Kronecker matrix products.

Inspec keywords: Lyapunov methods

Subjects: Stability in control theory

References

    1. 1)
      • S.G. Margolis , W.G. Vogt . Control engineering applications of V. I. Zubov's construction procedure for Lyapunov functions. IEEE Trans. , 104 - 113
    2. 2)
      • D.R. Ferguson . General power-series description of multiplicative nonlinear systems. Electron. Lett. , 450 - 452
    3. 3)
      • R.P. O'shea . The extension of Zubov's method to sample data control systems described by nonlinear autonomous difference equations. IEEE Trans. , 62 - 70
    4. 4)
      • R. Bellman . (1960) , Introduction to matrix analysis.
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