On the Number of Unstable Equilibrium Points on Spatially-Periodic Stability Boundary | IEEE Journals & Magazine | IEEE Xplore

On the Number of Unstable Equilibrium Points on Spatially-Periodic Stability Boundary


Abstract:

Unstable equilibrium points are fundamental in the study of dynamical systems, and can have various implications for nonlinear physical and engineering systems. In the pr...Show More

Abstract:

Unstable equilibrium points are fundamental in the study of dynamical systems, and can have various implications for nonlinear physical and engineering systems. In the present technical note, we derive lower bound as well as upper bound on the number of unstable equilibrium points on the stability boundary. For a class of nonlinear dynamical systems, by taking advantage of the spatial-periodicity, it is shown that there are at least (k + 1)Cnk typek equilibrium points on a stability boundary, where Cnk = n!/k!(n - k)!. Meanwhile, an upper bound is obtained by applying the Bézout's Theorem, when the system can be converted to polynomials by variable substitution.
Published in: IEEE Transactions on Automatic Control ( Volume: 61, Issue: 9, September 2016)
Page(s): 2553 - 2558
Date of Publication: 27 October 2015

ISSN Information:

Funding Agency:


References

References is not available for this document.