Geodesic
$\Psi$-asymptotic stability of non-linear matrix Lyapunov systems
Murty, M. S. N.1 ; Kumar, G. Suresh2
1 Department of Applied Mathematics, Acharya Nagarjuna University-Nuzvid Campus, Nuzvid-521201, Andhra Pradesh, India
2 Department of Mathematics, Koneru Lakshmaiah University, Vaddeswaram, Guntur, Andra Prdesh, India
Journal of nonlinear sciences and its applications, Tome 5 (2012) no. 2, p. 115-125.

Voir la notice de l'article provenant de la source International Scientific Research Publications

In this paper, first we convert the non-linear matrix Lyapunov system into a Kronecker product matrix system with the help of Kronecker product of matrices. Then, we obtain sufficient conditions for $\Psi$-asymptotic stability and $\Psi$-uniform stability of the trivial solutions of the corresponding Kronecker product system.
DOI : 10.22436/jnsa.005.02.05
Classification : 34D05, 49K15, 34C11
Keywords: Matrix Lyapunov system, Kronecker product, Fundamental matrix, \(\Psi\)-asymptotic stability, \(\Psi\)-(uniform) stability.

Murty, M. S. N. 1 ; Kumar, G. Suresh 2

1 Department of Applied Mathematics, Acharya Nagarjuna University-Nuzvid Campus, Nuzvid-521201, Andhra Pradesh, India
2 Department of Mathematics, Koneru Lakshmaiah University, Vaddeswaram, Guntur, Andra Prdesh, India 
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Murty, M. S. N.; Kumar, G. Suresh. \(\Psi\)-asymptotic stability of non-linear matrix Lyapunov systems. Journal of nonlinear sciences and its applications, Tome 5 (2012) no. 2, p. 115-125. doi : 10.22436/jnsa.005.02.05. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.005.02.05/

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