Research Article
Lyapunov Criteria and Localization of the Matrix Spectrum With Cassini Ovals
* Corresponding author
Abstract
This paper bridges Lyapunov stability theory with localization of the matrix spectrum using Cassini ovals, overcoming the conservatism of classical Gershgorin-based criteria. We establish conditions that completely ensure when the matrix spectrum is contained in the left half complex plane or within the unit disk. Furthermore, we show that the spectrum of the matrix belongs to the domain bounded by the Cassini oval is equivalent to the solubility of the matrix equation in the class of Hermitian positive definite matrices.
How to Cite
M. Rehman, S. Akram, R. Amna, T. H. Rasulov, A. Ubaydulloev, N. O. Juraeva, M. D. Daniyeva, S. A. Ikromova, Lyapunov Criteria and Localization of the Matrix Spectrum With Cassini Ovals, Int. J. Anal. Appl. 24 (2026), 283. https://doi.org/10.28924/2291-8639-24-2026-283
BibTeX
@article{Rehman2026,
author = {Rehman, Mutti and Akram, Saima and Amna, R. and Rasulov, T.H. and Ubaydulloev, A. and Juraeva, N. O. and Daniyeva, M. Dj. and Ikromova, S.A.},
title = {Lyapunov Criteria and Localization of the Matrix Spectrum With Cassini Ovals},
journal = {Int. J. Anal. Appl.},
volume = {24},
year = {2026},
pages = {283},
doi = {10.28924/2291-8639-24-2026-283}
}References
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