Results 211 to 220 of about 21,898 (243)
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Physical Review A, 1992
The definition of a Lyapunov exponent can be extended to include an imaginary part. This extension requires the definition of a coordinate frame on the tangent space of the differential equation and an extension of the concept of a limit. The definition of extended Lyapunov exponents is based on the eigenvalues of the fundamental matrix.
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The definition of a Lyapunov exponent can be extended to include an imaginary part. This extension requires the definition of a coordinate frame on the tangent space of the differential equation and an extension of the concept of a limit. The definition of extended Lyapunov exponents is based on the eigenvalues of the fundamental matrix.
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The calculation of lyapunov spectra
Physica D: Nonlinear Phenomena, 1987zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Greene, John M., Kim, Jin-Soo
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On inequalities of Lyapunov type
Applied Mathematics and Computation, 2003We generalize the classical Lyapunov inequality for second-order linear differential equations to nonlinear differential equations of second order and then to higher order linear differential equations.
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On the Construction of Lyapunov Functions
SIAM Journal on Applied Mathematics, 1969the same. These results are used to obtain new instability results for the Hill equation which extend the classical results of Lyapunov and Haupt. Finally, we show that a Lyapunov function for w' = 2Bw can be used to algorithmically obtain a Lyapunov function for y' = By along with certain verifiable conditions from which stability properties of y ...
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A Remark on a Theorem of Lyapunov
Canadian Mathematical Bulletin, 1970Consider the linear ordinary differential equation1where x ∊ En, the n-dimensional Euclidean space and A is an n × n constant matrix. Using a matrix result of Sylvester and a stability result of Perron, Lyapunov [4] established the following theorem which is basic in the stability theory of ordinary differential equations:Theorem (Lyapunov).
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SIAM Journal on Control, 1975
Consider the following infinite-dimensional extension of the linear control system discussed in Hermes and La Salle [9].Let T be a set (time interval),$\mathcal{S}$ a $\sigma $-algebra of subsets of T, X a quasi-complete locally convex topological vector space, and ${\bf m} = (m_i )$ a sequence of vector measures $m_i :\mathcal{S} \to X$, $i = 1,2 ...
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Consider the following infinite-dimensional extension of the linear control system discussed in Hermes and La Salle [9].Let T be a set (time interval),$\mathcal{S}$ a $\sigma $-algebra of subsets of T, X a quasi-complete locally convex topological vector space, and ${\bf m} = (m_i )$ a sequence of vector measures $m_i :\mathcal{S} \to X$, $i = 1,2 ...
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Journal of the London Mathematical Society, 1968
Kingman, J. F. C., Robertson, A. P.
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Kingman, J. F. C., Robertson, A. P.
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A Fuzzy Lyapunov Function Method to Stability Analysis of Fractional-Order T–S Fuzzy Systems
IEEE Transactions on Fuzzy Systems, 2022Xiaofei Fan, Zhanshan Wang
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