\(\Psi\)-asymptotic stability of non-linear matrix Lyapunov systems
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.
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
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M. S. N. Murty, G. Suresh Kumar, \(\Psi\)-asymptotic stability of non-linear matrix Lyapunov systems, Journal of Nonlinear Sciences and Applications, 5 (2012), no. 2, 115--125
Murty M. S. N., Kumar G. Suresh, \(\Psi\)-asymptotic stability of non-linear matrix Lyapunov systems. J. Nonlinear Sci. Appl. (2012); 5(2):115--125
Murty, M. S. N., Kumar, G. Suresh. "\(\Psi\)-asymptotic stability of non-linear matrix Lyapunov systems." Journal of Nonlinear Sciences and Applications, 5, no. 2 (2012): 115--125
- Matrix Lyapunov system
- Kronecker product
- Fundamental matrix
- \(\Psi\)-asymptotic stability
- \(\Psi\)-(uniform) stability.
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