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• W2895950520 abstract "In earlier works, solutions of Lyapunov equations were represented as sums of Hermitian matrices corresponding to individual eigenvalues of the system or their pairwise combinations. Each eigen-term in these expansions are called a sub-Gramian. In this paper, we derive spectral decompositions of the solutions of algebraic Lyapunov equations in a more general formulation using the residues of the resolvent of the dynamics matrix. The qualitative differences and advantages of the sub-Gramian approach are described in comparison with the traditional analysis of eigenvalues when estimating the proximity of a dynamical system to its stability boundary. These differences are illustrated by the example of a system with a multiple root and a system of two resonating oscillators. The proposed approach can be efficiently used to evaluate resonant interactions in large dynamical systems." @default.
• W2895950520 created "2018-10-26" @default.
• W2895950520 creator A5031429339 @default.
• W2895950520 creator A5053726952 @default.
• W2895950520 date "2018-01-01" @default.
• W2895950520 modified "2023-09-27" @default.
• W2895950520 title "Comparison of Sub-Gramian Analysis with Eigenvalue Analysis for Stability Estimation of Large Dynamical System" @default.
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• W2895950520 doi "https://doi.org/10.31857/s000523100001870-1" @default.
• W2895950520 hasPublicationYear "2018" @default.
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