# $\Psi$-asymptotic stability of non-linear matrix Lyapunov systems

Volume 5, Issue 2, pp 115--125 Publication Date: April 11, 2012
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### Authors

M. S. N. Murty - Department of Applied Mathematics, Acharya Nagarjuna University-Nuzvid Campus, Nuzvid-521201, Andhra Pradesh, India. G. Suresh Kumar - Department of Mathematics, Koneru Lakshmaiah University, Vaddeswaram, Guntur, Andra Prdesh, India.

### Abstract

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.

### Keywords

• Matrix Lyapunov system
• Kronecker product
• Fundamental matrix
• $\Psi$-asymptotic stability
• $\Psi$-(uniform) stability.

•  34D05
•  49K15
•  34C11

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