%0 Journal Article %T \(\Psi\)-asymptotic stability of non-linear matrix Lyapunov systems %A Murty, M. S. N. %A Kumar, G. Suresh %J Journal of Nonlinear Sciences and Applications %D 2012 %V 5 %N 2 %@ ISSN 2008-1901 %F Murty2012 %X 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. %9 journal article %R 10.22436/jnsa.005.02.05 %U http://dx.doi.org/10.22436/jnsa.005.02.05 %P 115--125