Lyapunov Criteria and Localization of the Matrix Spectrum With Cassini Ovals

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DOI: https://doi.org/10.28924/2291-8639-24-2026-283
Published: Sep 2, 2026
Cite as:
Mutti Rehman, Saima Akram, R. Amna, T.H. Rasulov, A. Ubaydulloev, N. O. Juraeva, M. Dj. Daniyeva, S.A. Ikromova, Lyapunov Criteria and Localization of the Matrix Spectrum With Cassini Ovals, Int. J. Anal. Appl., 24 (2026), 283.

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Mutti Rehman, Saima Akram, R. Amna, T.H. Rasulov, A. Ubaydulloev, N. O. Juraeva, M. Dj. Daniyeva, S.A. Ikromova

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.

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